Depending on how well you take care of your weave, you should be able to keep it in for 6-8 weeks. If you feel like your weave needs to be refreshed, you can go to a stylist to have your weave tightened and washed/styled.
It is possible for your hair type to be manageable and healthy, but that depends on you, and how you take care of yourself and your hair. Start by eating healthily, drinking lots of water and getting some kind of exercise.
As far as your hair, wash and condition it once a week. Give yourself hot oil treatments and deep conditioning treatments- alternate these, with hot oil one week and deep conditioning the next week. Also use protein treatments either the week before or the week after you relax your hair. Your stylist may be able to do this for you for an extra $10-$20. Get your dead/split ends trimmed (about 1/8 of an inch) every time you get a relaxer. Use as little heat as possible because curling irons and blowdryers can be damaging if used too much. Use products that have no alcohol (or little alcohol) because it is drying. This means staying away from spritz and hairspray. Oil sheen is okay though. Stay away from mineral oil as much as possible because this clogs the pores in the scalp. Other than that, use whatever products work for you. Elasta QP, Dudleys, Keracare, Mizani, Cream of Nature, Motions and Paul Mitchell are good product lines, but you don’t have to limit yourself to these lines. These are just popular brands for African American hair.
You can alternate between relaxing and weaves. The weaves will give you a break from styling and manipulating your hair too much.
Hope this helps.