Sticks wise you can pick up a Futaba 3GR with RX for £60-80, a Sanwa Gemini X with RX for around £100 and a Futaba T4GRS for around £150 all second hand. These are all 2.4GHz.
I'd deffo go brushless / lipo having been there and done that coming back after 30 years trying NiMh again first.
There's a super cheap BL 120A ESC at Hobbyking for £20-30 - depends when it's on offer. They come with a vanilla firmware but are a clone of the more expensive Hobbywing ESCs, and you can flash them with Hobbywing firmware to give you boost and turbo. I've two of these in mine and my lad's 2WD and they've been flawless so far, even running a 6.5 in my 2WD.
I've always bought 2nd hand lipos as well as budget is tight, you can pick them up for £10-30 each depending on spec/capacity. Same goes for motors, brushless need next to no maintenance other than possibly bearings. I've paid £10 for some 2nd hand in the past, up to £30 for a corker like new.
Don't forget to factor in a lipo compatible charger. I like the convenience of ones that can run 240VAC and 12V for trackside. There's a cheap IMAX B6 clone that does both, think I paid £25 for mine brand new.
Don't make the mistake of trying to future proof and start with a 6.5 - seen so many newbies at my local track try this and I always tell them they look like they are fighting the car. With new brushless stuff you can run a milder motor for the infield, and the ESC can add "turbo" which dynamically advances the timing on the fly when at full throtte for the straight.
Not all ESCs can do this though, the 10BL120 posted before doesn't have turbo and you can't upgrade it.