Track days and speed events (hillclimbing or sprinting) are the cheaper options and you can do them in an unmodified road car (though for speed events it has to be standard to be exempt from having safety modifications to the car).
Track days are probably the best place to start unless you want a competitive drive because you get a lot of time for your money compared to hillclimbing, which is about as expensive as motorsport gets on a cost per mile basis. Any hatchback or reasonably sporty saloon should be fine for the first few track days and the cost of track days at good circuits (Silverstone, Donnington etc.) typically only about £250 for a (weekend) day or £125 for a (weekday) evening session. If you want something a bit more nimble and don't want to take the risk of putting your everyday motor on the line you could look at getting something like a 205, Golf, E30 or MR2, all of which would be good track cars and convienently have been raced extensively in road legal spec so you could pick up a fully prepared car in reasonable condition with all the safety modifications needed for racing and hillclimbing but still realistically able to drive it to events and remove the logistical issue of a trailer and park it on the street just like any other car. You could do this with something more substancial if you wanted to, there are several Minis, a nice mk2 Escort and a 924 that live outside near me in this kind of hillclimb/track day spec.
Autotesting is cheap but very hard on cars, you're much more likely to end up with expensive repair bills and generally age your car quicker by doing autotests than trackdays.