When I play or GM Rifts there are a few things that I need to know. The first is whether the group wants to play a combat, social, or mixed game. The second is whether the group wants a high powered or low powered campaign. From the nature of your question I believe you wish to know how to rank characters in a high powered combat campaign on Rifts Earth which in my experience is the easiest style to rank them.
First thing to know is there are many aspects to combat. Because combat rounds last 15 seconds and many actions happen in that time some kinds of attacks will be much more effective then strait damage. Stunning attacks tend to be more effective at removing enemies from combat sense they tend to last a number of rounds, and any attack that knocks a character down will cost them an action. A stun can be more than enough time for an automatic hit on a called shot to the head in melee/point blank range. Like most game systems defensive capability and offensive capability have to be balanced out. To help with this my group breaks the characters down into three broad categories before ranking them Artillery, Heavy, and Light. I will first explain these categories, then I will give examples of some group tactics, and then I will give a numbered list of character classes by power.
Artillery is any character whose main/preferred combat option is to hang back and pepper the enemy from relative safety. Because of the safety element, this is the default position for non-combat utility characters (buffing/repairing/talking characters). Giant Robots using missiles, invisible/shielded/hidden Mages using ritual magic or summoned creatures, and snipers using stealth and confusion are all examples of Artillery characters. The jobs of this character are to deal as much damage as possible, watch for enemy reinforcement, apply debilitating effects to the enemy, and provide a “safe” fallback position. Giant robots and sometimes Glitter Boys fall into this category because they are expensive to repair and have excellent long range damage. Shifters and similar mages fall into this category because they have low average MDC (35-100) and spells that can totally change the nature of a battle, examples being Summon and Control Entity, Firequake, and Carpet of Adhesion.
A Heavy character is a tank and is expected to deal out solid damage while taking the majority of the enemy’s fire. The two most important aspects of this position are staying power and fire power. Combat Cyborgs with detachable heavy cyborg armor plating, power armor pilots with either good armor or flight capable, Baby Dragons with their MDC bio-regeneration, and Glitter Boys who have invested in a giant MDC shield are all examples of Heavy characters. The jobs of these characters is to be a solid and significant threat to the enemy, and draw enemy attention away from Light and Artillery characters. Power Armor and Cyborgs fall into this because they have solid armor (500-1000), good mobility, and can wield rail guns and other heavy MDC weapons. Baby Dragons and other high MDC creatures are this because they can tank damage without any cost sense it only takes a few minutes for them to completely heal from their wounds. If a Glitter Boy can regularly afford the costs of repairing damage he should be here because he represents a threat the enemy cannot ignore and will draw their attacks. Some creatures that have been summoned by mages will want to act as heavies sense they represent free MDC to the party.
A Light character is anyone who is acting as a normal soldier whether looking to get in close or take cover behind the Heavy you are expected to locate important and dangerous targets and eliminate them. Lights are also still at full strength when fighting in close quarters underground or inside buildings. Melee classes, very basic soldier classes, and most fast classes with auto-dodge fall here. Merc soldiers, who are not sniping, are here because they add attacks to the combat but are not a threat worth dedicating fire to. Melee Cyber Knights, Mind Melters, and other melee classes are expected to charge enemy artillery and stab optics, stun button mage’s heads, drop fusion blocks in the joints of robots or just climb on and cut the pilot out from the safety of their blind spots. Mages that use low level attack spells and buffing spells will often find themselves doing the same job as other Light characters.
As for tactics it is generally important to use the correct level of response to most threats. Unlike D&D where engagements do not cost you anything so long as you survive resources are harder to come by in rifts. So if at all possible pick your fights. A group of bandits on the road are better handled by the party’s Light players and Bio-Regenerators. Lights can more easily replace their armor, and psychic and magic shielding will absorb the bandits low MD to mitigate the cost of such a venture.
If your group has multiple power armor, robots, etc. they are in little danger of being ambushed but will have a very hard time fighting in doors or underground. It is generally best for a party to only have one giant robot, if any as they are expensive to maintain, and power armor pilots should look for suits with detachable wings and missile pods. For power armor I recommend acquiring a giant MDC shield as it is much cheaper to replace/repair. If anyone in the group is willing to play an operator, psi-tech, or specialize themselves as a mechanic/engineer it can go a long way towards cheapening combat for the whole group.
Magic is your friend, use it! Unless the group is decidedly against magic it is best to take advantage of some simple buffs. Invisibility will leave many opponents unable to effectively fight back. Magical Adrenal Rush, Giant, and Speed Weapon can turn your melee characters into monsters with 14 attacks per melee round or 28 if they have paired weapons (5 normal +2 adrenal rush, doubled by speed weapon and doubled again by having paired weapons). Spells like Armor of Ithan, Armor Bizarre, and Impervious to Energy can make your party nice and tanky without costing much. Just remember to read the rules on magic there are allot of ways to get enough PPE to cast two or three big spells per combat, or a dozen of the cheap ones.
Remember that most enemies that are using MD weapons and armor cannot themselves do MD. If one of your players has the psychic power Kinesis it can be useful to disarm your opponents, and if anyone in your group is playing a melee fighter disarming can also be viable for you. Once disarmed, most enemies will have no way to deal damage to your group. Spells that trap enemies, neural maces which can stun your opponent, and anything that knocks you down can have the desired effect of capitalizing on a fight’s action economy. Most opponents will have 4-6 actions per melee round. Things like Horror Factor can remove one action from you at the beginning of each melee round. Remember that the same thing works on your opponent so use it. Knock down effects also remove an action, and require another to stand, but also drop an opponent to the bottom of the initiative.
In my experience the best mix for a group is one or two utility characters and two to three combat characters. If you have a group of five and everyone wants to play a combat character I recommend one Artillery, one or two Heavy, and two or three Light. Psionics are not necessary but it is very helpful for one guy to have Sixth Sense, Presence Sense, and See the Invisible. Magic is recommended for at least one character, or two characters with vastly different styles. This break down allows the group to work well in the open and in close quarters, and also helps to give allot of options.
Power Tiers, from least to most, for High Powered Combat Oriented Rifts Earth Campaigns.
5th Tier (none combat and basic troops): Rogue Scholar, Rogue Scientist, Cyber-Doc, City Rat, Body Fixer, Saloon Bum, Saloon Girl, Vagabond, Wilderness Scout, Merc Soldier, Operator, Dog-Boy, all civilian classes, and any military class that has no special abilities.
4th Tier (elite troops and low MDC creatures): Cyber-Knight, most psychic classes, Combat Magi, Ley-Line Walkers, normal Mystics, most Samurai and Ninjas, Crazies, Juicers, most native americans, lightly armored cyborgs, all western gunmen, most intelligent D-Bees, animal D-Bees with less than 500 MDC, any military footslogger with one or two good special abilities, and tier 5 characters with access to dimension book arms.
3rd Tier (high MDC threats and dangerous magic): Power Armor Pilot, Glitter Boy, Mystic Knights, heavily armored cyborgs, Baby Dragon, Robot Pilot, Shifter, High Magus, Lord Magus, native americans with powerful fetishes, Most D-bees with impressive abilities and high MDC (200-1000), combos between a MDC RCC and a Tier 4 OCC, most characters with super powers, and tier 4 characters with access to dimension book arms.
2nd Tier (the most power any player should have): Godlings, most Adult Dragons, Techno-Wizards (unless they have been reined in or neglected), highly optimized robots, small spacecraft, very high level magic casters, and most creatures with 2.5-5k MDC.
1st Tier (subjective and NPC): anything more powerful.
Be careful with this though. Most classes are not optimized and can jump tiers with a little work. example: a starting Psi-Tech is at the lesser end of tier 4, however if they can get access to power armor pilot elite and a SAMAS they can jump strait to tier 2.