The M3 is built for this - 414–503 bhp, rear-wheel-drive, and one of the finest chassis in the world. The F80 Competition is the used sweet spot (£30,000–£40,000); the G80 is the future. Buy the newest S58 you can afford, or hunt for a well-maintained F80 Competition with the crank hub done.
The E46 M3 with the S54 is the greatest M3 ever made - a future classic that's already appreciating. The E90 M3 with the S65 is the only V8 M3 - a masterpiece that will be remembered as one of the greatest naturally-aspirated engines ever built. Both are worth proper investment.
The M3 is a daily-drivable performance car - the F80 and G80 are comfortable, practical, and have four doors (unlike the M4). The F80 is the better daily driver; the G80 is more refined. The E46 and E90 are weekend cars.
The M3 is one of the best track-day cars you can buy - the E90's V8 is a track-day hero; the F80's turbo torque is addictive; the G80 is the fastest. Budget for cooling upgrades and preventative maintenance.
A £15,000 E46 M3 is the entry point - but budget for VANOS (£1,500–£3,000) and rod bearings (£2,500–£4,000) before you buy. A £20,000 E90 M3 is the V8 entry point - but budget for rod bearings (£2,500–£4,000) before you buy. The F80 Competition at £30,000–£40,000 is the value sweet spot - 444 bhp, proven engine, and the crank hub is the only caveat.