Guess what! This has its own guide! Check it out
You ideally want generals that have double or triple buffs as your attack General. Unfortunately not many of these are available in the Tavern and probably (most likely) never will be. You're better off waiting to get fragments of someone better, or splurging and buying up the ladder and hopefully getting someone good from the $100 pack.
The only Attack General even worth a dam that you can buy from the Tavern is Trajan. And that's because there's only one other real Ground General in the Event Packs (Scipio).
If you're not spending enough money to hopefully get at least one good Attack General from Event Packs, just hunker down, don't waste Gold and Gems beefing up subpar Generals. You will eventually get someone worth it from Fragments. In the meantime, work on your Defense, do a bunch of Research, and keep upgrading your Keep.
Your next stop for Generals should be Debuff Generals. These General's "Special Skill" reduce the troop stats of your enemies troops. These are amazing because they are the only general skills that work from the sub city mayor slots when you're attacking and defending. Stacking Generals with Debuffs in all of your Subordinate Cities can decrease your enemies stats by hundreds of percentage points and will give you an advantage in battle, or more realistically, put you on a level playing field with everyone else who has Debuff Generals in their Sub Cities. Here are the 6 best (in my opinion) that you can buy from the Tavern. With Nero, Andrew Jackson, and Empress Cixi being the best of those 6.
Double Drop Generals
Get the most bang for your buck (stamina) and pick yourself up a couple Double Drop Generals. Preferably Baibars but if Cleopatra shows up at your door cold, scared, alone, followed by who knows what, don't turn her away. Eventually you can kick her out and replace her when you're blessed by Baibar's appearance in your .
yeah, you want 5(6!) of her to maximize farming returns while you're offline!