OK this will be my first turtle and I need some help about what to get for my new friend.
1.What size tank should I start off with? I really don't want to go over a 20 gal.
A 20 gal is OK to start with but will need at least a 40 gal breeder when bigger.
2.Do I need a basking spot lamp?
Yes you do need a basking spot lamp to go over a basking spot area, somewhere for you res to haul out onto and dry off. the basking spot can be pile of rocks, big stone, or turtle dock.
3.What should I feed him?
Juveniles are mainly carnivorous, and become more omnivorous as they reach adulthood. The diet should be balanced and include a variety of meat-based protein sources and fresh plant material. Do not rely simply on commercial diets. Juveniles should be fed daily, whereas, adults can be fed every other day. Turtles are messy eaters so it is best to move the turtle to a separate feeding tank. This may also help reduce the amount the turtle defecates in the water of his cage. Allow the turtle to eat for 15 minutes before moving it back to the aquarium.
INGREDIENTS
EACH meal should contain ingredients from the following categories:
Commercial diets
(Less than 25% of the diet) Trout chow
High quality, reduced-fat, dog kibble (occasionally)
Commercial floating pellets or sticks for fish, reptiles, or turtles
Animal protein
(Less than 25% of the diet for adults) Live feeder fish (occasionally)
Earthworms
Finely chopped raw lean beef or beef heart
Cooked chicken
Snails
Tubifex worms
Meal worms
Wax worms
Pinkie mice
Crickets
Blood worms
Vegetation
(50% or more of the diet) Collard greens
Mustard greens
Dandelions
Carrots (shredded root and top)
Squash
Green beans
Sweet potatoes
Apples (shredded)
Melon
Berries
Bananas
Grapes
Tomatoes
Plums, peaches, nectarines (NO PITS)
Supplements Dust all foods at each feeding with a general high ratio calcium-mineral supplement containing Vitamin D-3 such as Rep-Cal or Miner-All
Use a vitamin supplement twice a week
Offer cuttlefish bone as another calcium source. I also use calcium flour as a very high in calcium but you can get suppliments high in the help of D3.
4.What should I keep the temp at?
You need to keep the water temperature between 74f and 80f will need to heat in the colder seasons using a submersible aquarium heater. The basking spot needs to be around 85f to 95f. The basking lamp will warm up the water so the use of a thermometer will be needed.
5.Do they grow fast?
Yes the grow very fast in the first few years. Takes around 5-7 years to reach full adulthood. Can grow up 12 inches if it's a female and few inches shorter if a male. so prob would be an idea getting the bigger tank to start off with.
You will also need a uvb/uva fluorescent light, to enhance the turtle's production of Vitamin D-3, and provide it with a more natural habitat. Bulbs must be replaced after 6 months, as their ability to emit true full-spectrum light diminishes over time. The light source should be within 18-24 inches of the turtle. The light should shine directly on the turtle, and not be filtered through glass or plastic. It should be on a timer so the turtle has a normal day-night cycle.
The most expensive item you will probably buy is a filter as you will need to try and get the biggest and best filter you can possibly afford try and get at least twice the the size filter for your tank as your res will produce a lot of waste which will involve a weekly water change as they live swim drink the water they are in.
Heres a link to have a read of to get you going. Good Luck
Andy 
RES INFO