As a practical prepper (not doomsday), I have keflex & bactrim (sulfamethoxazole and trimethoprim) allergy, what type of antibiotics can I stockpile/take safely?

It depends. Bactrim (sulfamethoxazole and trimethoprim) is a mixture of sulfamethoxsazle and trimethoprim. Most people are allergic only to the sulfa component. Keflex (cephalexin) may cause rashes without an allergic mechanism. Without knowing what kind of reactions you had to these antibiotics, there is no sensible way of answering you. See an allergist to sort out whether you are really allergic and then discuss with him/her how to proceed.
Many things. You can use: 1. Macrolides like zpak, biaxin 2. Quinolones like avelox, cipro 3. Tetracyclines like vibramycin, doxyxcycline 4. Misc like Clindamycin and Chloramphenicol (many side effects here) avoid 1. Penicillins - may cross react with keflex 2. Cephalosporins - will cross react with keflex 3. Sulfa medicines like septra - cross reacts with bactrim (sulfamethoxazole and trimethoprim).