There are two reasons you don't want to piss away a lot of money on fancy pumps and stuff like that. First, it may not be legal. Second, if it is legal all the buddies around you that you are racing tend to hit each other. One smack in the wall and you'll be shelling out a lot of dough to replace those parts. So no, it's not an area you'd want to put your money in.
When someone comes in and wants to get into racing we'd steer them to a nice car that is for sale. By nice I mean one that we know is setup for the track they want to run on and handles well. Spending the money up front on a car that is well sorted out I think is the best investment. You will most likely have a spec on the tires you will have to run and fresh tires are a plus. Good shocks are also a plus but there will also be a spec on these. Spec meaning the rules will dictate the type/style.
On the engine, yes keep it simple. The first year you will be learning the ropes. Not having a ton of power will help you learn the car and work on what it likes and doesn't like.
Claiming is a rule that allows another racer to "claim" parts off your car. The purpose of the rule is to keep trick hidden stuff, or obvious for that matter, parts out of the car. Lets say you build a super trick motor with all the lightest and best bottom end components. A racer could have $3000 in crank, rods, pistons, coatings. If a claim rule exists where another racer can put up $1000 for the guys motor, the logic is folks won't build that stuff. Claim rules though are seldom if ever used in our area. The reason is if one person does it, the next week they can, and will be claimed. Plus whoever does it will probably get the crap beat out of him in the pits.