It seems 15 EK/5 Warlock (to get Haste/Fireball) or 5 Champion/15 Warlock (to get the extra attack) are your best bets, if you want to have the highest AC possible and focus on weapon damage. The former gets 3 attacks per round, fewer spells/slots (but gets Haste twice per short rest); the latter gets 2 attacks per round, more spells/invocations (not Haste though), expanded crit range, and much higher spell slots (L8).
Different build options
A few ideas, each with a slightly different balance between raw damage (with the Attack action), AC, and versatility:
- Stick to Eldritch Knight with 3 levels of Tome Warlock, netting you Book of Ancient Secrets. You would get 3 attacks, plus some sweet spells/slots that recharge on a short rest (and you can use your 'Lock slots to cast EK spells).
Pros: Most straightforward/simple way to get what you want, also has the highest AC (if you pick +1 AC Fighter feature). You get Constitution proficiency, making it easier to maintain buffs if you take damage. Has 1 more attack than the other builds, and the only one that can get Haste (if you go 15 EK, 5 'Lock, in which case you can cast Haste 2/short rest) Cons: Not as versatile as the others, fewer/lower level spell slots (you don't even get L4 slots), you give up a Feat/Ability Increase.
- Same as above (3 Levels of Lock), but with Arcane Trickster. Sure, you only get 1 attack, but it comes with a 9d6 Sneak Attack (assuming there's another melee PC who'll be adjacent to your enemies). You also get Spell Thief, which can be pretty cool. Pros: Probably the sweet spot between versatility and damage (see below for more details), though in terms of spells, you only get 2 L2 slots (which recover on a short rest) Cons: Has the lowest AC of the 4 builds.
- 15 L of Warlock, 5 Levels of Champion Fighter (or any other class that grants an extra attack at L5--Barbarian, Paladin, Druid, Ranger, Monk). The advantage with Fighter is that you get heavy armour proficiency, martial weapon proficiency, AND can get Two-Weapon Fighting. Pros: Can have the highest AC (same as #1), access to higher-level spells than EK, and these recover on a short rest. Also, since you won't be going EK (inefficient, leads to MAD, no access to Haste until L13), you can grab Champion and be able to crit on a 19-20. Cons: You lose a feat/ability score increase, and 9th level spells (though you don't have these with #1 or #2). You also lose access to Wizard spells, but if you wanted stuff like Fireball, Scorching Ray, Counterspell, those are also in the Warlock list.
- 14 L of Warlock, 6 Levels of Bard (College of Valour): Hands down the most versatile. Both classes use Cha as their main stat, so, all of your abilities will be at full force. One amazing advantage (IMHO) is that you get plenty of healing every short rest (using 'lock slots to cast Bard spells at higher levels). You give up on L8 and L9 spells, but you didn't have those with EK or AT. I haven't done a thorough analysis of the spell selection/combos, but there should be plenty of interesting possibilities. Plus, if you can't engage in melee (for whatever reason), you have Eldritch Blast (at 4d10 + 20 damage, if you grab Agonizing Blast). Pros: Largest spell selection, including healing, buffing, debuffing, and damage. Cons: Less AC than 1 or 3, less weapon damage than 1-3.
The first two provide the most raw damage, the last two the most versatility (with #4 giving a huge range of spells to choose from). I think #2 is probably a really great sweet spot between damage and versatility (since Rogues get to add Sneak Attack damage to their reaction attacks), but with the lowest AC. So, if you grabbed the Sentinel feat, for example, you're almost guaranteed to be handing out some extra pain, even outside your turn. If you managed to grab Sentinel and Defensive Duelist, with a Rapier, you'd put your reaction to good use every turn: either the enemy attacks you, in which case you use DD if they hit; or they attack your ally, and you make a melee weapon attack; or they try to move away, and you make an opportunity attack. All of these with an extra 9d6... However, as noted above, this build has the lowest AC, and the spell slots available will probably not be enough to keep you in the front lines.
Summary of options
- has the most AC (together with #3), the most attacks per Action, and with the 15 EK/5 'Lock, you can cast Haste on yourself (or Hex on an enemy) twice per short rest.
- has the most weapon damage, but the lowest AC. I don't think it would be very viable, barring some items from the DMG massively boosting AC.
- is probably the more 'robust' build--you can get the highest AC possible, 1 fewer attack than #1, but expanded crit range, and a bunch more spells (and higher level slots that recover on a short rest). You don't get Haste though, but in terms of damage, Hex is better.
- has lower AC than #1 and #3 (by quite a few points), but much more spells and can go on without a long rest for quite a while (in theory, since you'll be recovering slots that can be used for healing, and you have Song of Rest. However, if you end up taking too much damage due to low AC, you might use up all your spell slots for healing).
Hope this helps. If you want general guidelines on which class to pick first, I posted some guidelines here. Considering just the 4 combinations above, Warlock is never the best choice as your first class. If you plan to use spells requiring Concentration (e.g., Haste), L1 Fighter gives you proficiency with Constitution saving throws.
Advantages over Ritual Caster
Quite a few advantages, IMHO, though whether they contribute to your build depends on the nitty gritty of what you have in mind:
- You can grab rituals from any class, but they all use Cha instead of whatever the original class uses (so, greater selection and if you have high Cha, they're all pretty effective; though note that if you go 15 EK / 5 lock, you can only pick rituals up to level 3).
- You get 3 cantrips from any class, and they use Cha as well. A few that could be useful for your build: Thorn Whip (can pull enemies towards you, from 30 ft away; esp. effective with EK's Arcane Charge), Vicious Mockery (psychic damage, targets Wis, gives disadvantage), Shocking Grasp (attacks with advantage vs. metal armor, denies enemy's reaction), Ray of Frost (reduces enemy's speed).
- You can get Eldritch Blast + Agonizing Blast + Repelling Blast (push an enemy away up to 10 feet per hit; so, max 40 feet, if you hit with all 4 rays), which is the best ranged cantrip (in case you NEED to attack from afar). Together with Thorn Whip, you'd have a lot of battlefield control, pushing and pulling enemies into bad positions/away from the squishies.
- You can cast Haste on yourself twice per short rest (you get Haste with EK after L13, and 'Locks get 2 L3 slots that recharge on a short rest starting L5). A L20 EK can cast Haste at most 4 times per day; a L15 EK / 5 Lock can cast Haste at least 4 times per day.
- Note that Book of Ancient Secrets allows you to copy ritual spells that are up to half your levels in Warlock, rounded up. The highest ritual spell is L6, not sure if there's a specific spell you want to get. Plus, you can get Warlock rituals 'for free' (i.e., if you pick them at level up, you can cast them as rituals; and can then grab other classes' rituals using the Invocation).
- You also get access to Hex, which adds an extra 1d6 damage per hit, and the target has disadvantage on ability checks of your choice. Unfortunately, you can't have Haste and Hex active at the same time. So, Haste gives you an extra 1d6 + Dex/Str Mod (or an extra action to use some other way), whereas Hex gives you an extra 4d6 (3d6 from each main-hand attack, and 1d6 from off-hand attack). Haste gives you more options (you get to attack and Disengage/Dodge, if needed), Hex gives more pure damage.
- Note that with Hex, you can get about the same weapon damage as a L20 EK with Haste (see anydice analysis; the graph is easier to read than the table). Output 1 is a TWF EK with Haste attacking 6 times with a Rapier, Output 2 is a TWF 15 EK/5 Lock with Hex attacking 4 times--the average weapon damage is 57 for the EK, 52 for the EK/Lock. If you go with the 5 Champion/15 Lock build, you have an expanded crit range of 19-20, and whenever you crit, Hex dice are also re-rolled (see also a new build, at the end). Also, the same analysis about Haste castings per day applies to Evocation spells/day: a L20 EK can cast Fireball at most 4 times per day (once at L4), this build can cast Fireball 2/day + 2/short rest.
In short, you get your spellbook without sacrificing damage, you get more castings per day of your 3rd level spells (which are EK's second highest slots anyway), and access to rituals and cantrips from any class (and these use just one stat); all of which, in my opinion, are a strengthening of the main class (i.e., there's good synergy). Losing a feat due to L5 Warlock is actually a non-issue because taking Ritual Caster also costs a feat. If you don't mind giving up Wizard spells (via EK), one other build that just occurred to me is 15 Champion/5 Warlock: at L15, a Champion can get +1 AC (via L10 feature) and can crit on an 18-20, which, together with Hex, can mean a boatload of potential damage. The downside is that, except for cantrips and rituals, you'd only get Warlock spells.