These days it is only worth using brushless! (Despite what you've said!)
Why wouldn't you choose to spend your hard earned on a motor/speedo that you can fit to your car and never do any maintenance on, that runs more reliably and efficiently and is more readily available...and will still be running just as well once you've improved?
There really is no point in going back to brushed these days!!!
You have 2 options with brushless....sensored or sensorless.
Sensorless is cheaper, is a simple motor attached to ESC via 3 motor wires setup. Can be bought pretty cheaply and will be more than good enough to get you back into it. You can then buy sensorless motors of different ratings to help control your speed as you improve. Look up the EZRUN systems, I think they are pretty popular.
Sensored systems are more expensive, but offer a smoother/more controlled power delivery at low speeds as there is an extra set of wires between motor and ESC that tell the ESC where the rotor is at all times. At low speeds the timing is controlled to ensure smooth response. Speed passion are pretty popular and reasonably priced for this, although i run a Nosram ESC and Novak motor and it's been a bombproof setup so far!
Most regular racers opt for the sensored systems ultimately, but I also know a lot on this forum use the sensorless ones without any issue, and the systems are improving all the time. It used to be that sensorless systems suffered quite badly from 'cogging' where at low speeds it stutters. But proper gearing and newer systems are better at avoiding/controlling things.
Personally I skipped sensorless and went straight for sensored from the outset. Bought a 2nd hand ESC and a 10.5 turn motor (which at that point was roughly equivalent to a decent 19t brushed motor) and loved it. Perfect to learn on. I now run 6.5/7.5/8.5 motors as I've improved. Spend the money once rather than buying stuff twice would be my advice! It might be more expensive, but the payoff is worth it if you intend to stick at it.
That's about all on that side...as for batteries, again, don't go back! Go Lipo and love the no cycling, longer run times, longer battery life and the need to have only 1 pack per car for all your racing!
Hope it helps and have fun!