Since you mentioned mage spells, I will answer in a mage's perspective.
In short: Use more cantrips, and adapt to the situation. Most of all, cooperate.
Use more cantrips
1. How can a mage learn new cantrips after character creation?
Since cantrips are spells, and the mage can add two new spells to his or her spellbook each level, a mage can choose cantrips for these spells. Likewise, the mage could copy a cantrip off of a scroll, if one exists, or out of another wizard’s spellbook. The mage can obtain new cantrips just like he or she gains new spells of 1st level or higher.
(Source: D&D Next Q&A: 10/10/13.)
RAW, you have no limit on how many cantrips you can learn. The rules just state that you start with three cantrips initially, and it is not a hard limit. Sure, cantrips can only produce negligible effects compared to spells with levels, but your character (and probably yourself, because you have gone through all the burden to play a spellcaster) is smart, and a smart person like that can surely make creative use of mere cantrips. For example,
- Dancing lights can be a good warning signal to your allies.
- With mage hand, you can deliver all the good spells like mage armor to your comrades.
- Mending can be used to fix a mundane item with minor flaws. Good for roleplaying.
Of course, you can instead do offense with cantrips and prepare more leveled spells for utility. For instance, aside from dealing damage, ray of frost also slows the opponent. This effectively prevents him from coming through the battlefield and cutting weak party members while your meat shield is holding him off.
Campaign-dependent: Reduce your need for spells by obtaining proper items
For example, with Elven Chain and other party members having decent AC, you wouldn't have to prepare mage armor, because your AC is already equal to what mage armor can provide, and probably you are the one with the lowest AC in the party. Likewise, proper magic items can reduce the need of certain spells, or something like Ioun Stones can even remedy the situation immediately. Of course, this is campaign-dependent because loot is entirely dependent on your DM's discretion.
If you are that desperate, then multiclass
If everything fails, there is always the final place for refugee: Multiclassing. Taking a dip in another spellcasting class will net more kinds of low-level spells in your reservoire. (Also note that some spells like cure wounds can be actually cast at higher levels even if you have only one level on the class which gives it, RAW.) Taking a dip in a class with heavy armor proficiency will virtually remove your need for mage armor. Of course, you lose awesome features of a high-level mage, but if you badly need more spells (or less trivial spells), then you should give it a try.
Don't try to do everything
If you are not soloing, you will probably have other party members, and I suppose one of them will be another spellcaster. Talk with her. Unless she is an offense-oriented hybrid caster like a paladin, probably your area and her area will overlap. Debate with her, and fix your role. You can save your grease when your druid friend will instead cast entangle for you.
Post Script: DON'T mind the levels
Even you have admitted that spell levels are less relevent in D&D Next. In 3.PF, hold person is inferior to hold monster even if you use it to a person, because lower-level spells actually have lower save DCs. However, in Next, they have the same save DCs, so hold monster is only truly effective against non-humanoids. Also, some spells can be cast on a higher level for stronger effects. For example, magic weapon gets its enhancement bonus upgraded when cast with higher level slots. Do not think the spells as "Nth-level defense/offense/utility". Rather, mind the roles of the spells. If you prepared grease to abruptly stop enemies and ray of enfeeblement to weaken the brute coming, that's fine. If you prepared them just to fill "1st-level offense" and "2nd-level offense", don't. By regarding the spells as roles instead of levels and categories, you'll find out that there is actually much space to squeeze in your daily preparation limit.