In order to both drift and race successfully, you need to have a good understanding of the geometry of the car, ideally having built it yourself. They really are not challenging to build. Also, you have not allocated enough budget for even a kit that you could race, let alone an RTR. The RTRs you can get for that amount of money will perform poorly, but adequately, depending on your expectations. They will not be raceworthy, but may drift ok. Which brings me to the thing about changing only tires...that's not possible I'm afraid. A car setup for drifting, on grip tires on a track would be terrible. Similarly a car setup for track use would be extremely challenging to drift smoothly. It really can't be done, the two setups are completely opposite. You could do it by having another set of all 4 shock absorbers and 2 rear differentials, as well as the tires, but those are the minimum parts you would need to swap to change its role.
If you really are interested in getting into the on-road hobby I strongly recommend saving a few more bucks and getting something good, ideally that you can build.
The drift RTRs are a little more expensive, but at least they do what they are supposed to do well, drift. This is because you don't need high end electronics to drift. The normal grip cars are a little cheaper, but they have almost the same electronics, which are frankly inadequate for een just going fast outside the house. Their speed is not impressive. You need a brushless motor to go fast, and RTRs with brushless are somewhat more than you have to spend, especially if you need to buy a charger too.
Try one of these to start with...
That is as cheap as I would ever go, and this car is not without its own minor issues. If you decided to wait and save a few more bucks, you could get this...
The Sprint 2 is a much better car than the E10 and more importantly comes with a 2.4ghz radio, which means you will never lose control of the car to interference, and get more range than the AM radio included in the E10.
In any case, the sprint 2 is the better platform to later put a cheap brushless set into.