What do you mean by "proper tires"? One thing about the stock suspension is that it is optimized for the stock AD07 tires. Once you start using stickier tires, you run the risk of riding on the bump stops and overwhelming the suspension. That being said, AD07 tires are pretty good for a street tire...I would give them a shot at the track if you are sticking with an otherwise stock Elise. Once you start going to stickier tires, then you need to upgrade the suspension accordingly.
With base suspension and AD07 tires, you might not need a baffled oil pan, though I will defer to the experts on this one. Ditto fuel starvation issue. You can literally drive a stock Elise onto the race track from the showroom floor and it will do pretty well.
To all of the above, I would probably also consider changing your battery. The stock battery can leak and you can easily save 10 .lbs by going to a lower capacity sealed unit. This is not totally necessary but is good for peace of mind. Consider getting the car aligned, make sure everything is tightened down, and have fun!