Moving on to your points about the batteries and electrics. Don't go budget, it's pointless for racing. Mid range is fine, most of my electrics are mid range and my car is just and quick and responsive as the rest of the field.
Decent motor (but you will need a faster one once you've got the hang of 5 minutes with no crashing):
https://www.rccarshop.co.uk/rp0010-rp540-8-5-turn-540-sensored-brushless-modified-motor-brca-legal-p
This ESC is good enough for club racing (I did a few regionals with one in and it was fine):
https://www.rccarshop.co.uk/hw30125000-quicrun-10bl120-sensored-p
If your feeling flush then this ESC is better (you can add boost and turbo), but it's 3 times the price of the one above, I use these in my current race cars:
https://www.rccarshop.co.uk/HW30112600-HOBBYWING-XERUN-XR10-PRO-SPEED-CONTROL-BLACK
Servo will depend on the car you pick, as some cars can't take full size servos, but this would work in just about any 2WD buggy:
https://www.rccarshop.co.uk/srt-ch6012-srt-ch6012-hv-cl-servo-9-0kg-0-07-sec-at-6v-semi-m-case-p
Radio depends on if you want a stick radio, or a wheel. There's a lot more choice for wheel radios but some people just can't get on with them if they used sticks as a kid.
These batteries are good, and it would also have enough capacity for 4wd, you will need 2 packs minimum, preferably 3 so you can allow them a bit of rest between coming out of the car and gong back on the charger (this is not essential but can be the difference between them lasting a couple of seasons vs 4 or more seasons):
https://www.rccarshop.co.uk/IPBL2S4400MC3-Intellect-LiPo-LiHV-4400mAh-2S-18-5mm-Shorty-7-6v
For the charger, these are great, as you can charge 2 packs at once which really helps when getting ready to go to racing:
https://www.rccarshop.co.uk/sk-100162-sky-rc-t100-battery-charger-p