Core books + complete series is what I find to be the "typical" set of books -- lots of options, not too terribly broken. The "Races of ..." series and the elements series (Frostburn, etc.) are a little more outside of my realm of knowledge. There are really a
lot of official books. Maybe over 100 3.5 edition books if you include all the setting-specific books. There is a list somewhere on the official site.
If I had $50, yikes, that's maybe only good for 2 books. I just looked on both Amazon & eBay, and the only 3.5 edition WotC hardcover that is under $15 is Complete Warrior (on both sites). If you're careful, you might be able to get 3 books for $50. Here is my summary:
- Complete Arcane: Introduces the warmage, wu jen, and warlock classes (warlock can do very limited magic, but can do it over & over again). Introduces draconic feats for sorcerers, extra metamagic feats for neat effects, and new "sudden metamagic" feats (these allow a spellcaster to apply metamagic on the fly without planning ahead).
- Complete Mage: Introduces "Reserve Feats" -- these allow spellcasters to have a single weak but never-depleted spell. This is important if you dislike the "15 minute adventuring day" (where the players sleep after every battle to regain spells). Having a simple blasty attack means the spellcasters can keep going even when their limited normal spells have run out. Also offers alternative class builds (give up a class feature to get something new, such as a sorcerer giving up a spell to get +2 HP per level).
- Complete Adventurer: Introduces scout, ninja, and spellthief classes. Tons of feats for bards, even some for fighters & barbarians.
- Complete Scoundrel: Introduces luck feats (allow for re-rolls when the dice are not on your side), ambush feats (allow rogues to trade sneak attack damage for various combat advantages), and skill tricks, which expand how skills are used.
- Complete Divine: Introduces favored soul, shugenja, and spirit shaman classes. Has an expanded list of deities & portfolios for clerics, along with a lot of new deity domains. I'm a fan of the oracle domain, as it gives clerics the identify spell at level 1, and access to the scrying spell a level earlier than normal. It also introduces divine feats, which allow a character to swap daily uses of turn undead for other supernatural abilities. This is where divine metamagic comes from, and this is how clerics become powerful fast. Also introduces wild feats, which work like divine feats, but for druids.
- Complete Champion: Has interesting divine alternative class builds (such as a rogue giving up his/her trap sense feature, and getting the ability to sneak attack the undead). Introduces domain feats, which grant supernatural abilities based upon the cleric/god domains, but with no prerequisites so anyone can take them. Has more reserve feats & wild feats too.
- Complete Warrior: Introduces the hexblade, samurai, and swashbuckler classes. Also has boatloads of feats for martial classes such as the fighter & barbarian. I like the ranged disarm feat -- the king says "disarm them" and suddenly the players are surprised to see that their weapons are shot out of their hands. Introduces weapon style feats that really do encourage fighters to develop a style of fighting.
- Player's Handbook 2: This is lumped with the Complete Warrior because many people think it was originally intended to be the companion book. Offers alternative class builds, such as the ranger that gives up his animal companion in exchange for being able to flank with ranged weapons. Has lots of general feats for mid-level characters, and a handful of high-level feats for fighters. Has good new spells for various classes, and introduces the rebuilding rules (for re-doing your character without having to start over).
- Spell Compendium: I didn't mention the spells that in the other books (except the PHB 2) because most of them are compiled here. This book makes spellcasters of all types even more diverse and interesting than before.
- Magic Item Compendium: Likewise, while there are many magic items scattered throughout many books, this compiles a huge number of them. I like this book a lot, though I feel healing belts are underpriced.
My suggestions are as follows. Get the Spell Compendium & Magic Item Compendium first, because you can likely only get 2 books, so you might as well get the "best of" books. If you can get something beyond that, go for the Player's Handbook 2, as there is a little bit for everyone in there. After that, personally I'd want Complete Adventurer even though I didn't write much about it -- I simply love bards, so I must have that book. You mileage may vary. For you, perhaps the reserve feats in Complete Mage or the weapon style feats in Complete Warrior, depending upon whether you see wizards or warriors as needing a boost in your campaign.
If you
really see warriors as needing a boost, though, you'll probably want to look into the Book of 9 Swords (aka Tome of Battle) -- it is all about martial classes on steroids. I haven't used it, though, so I have few ideas about it yet.
Have fun!