I too am reading up on the basics of gunsmithing and whats involved. Anyway, check out
http://www.youtube.com/watch?v=hYnjRvT6t44
He has lots of videos that talk about gunsmithing for accuracy.
And I agree that your 243 cannot be turned into a 338Lapua.
If you don't reload, go buy a reloading manual. Not for the powder loads, but just to have the dimensions of every case. Based off the question you are asking, you aren't aware of the differences between a long action and short action rifle. Look at the difference in the bolt length between a 308 and 30-06. The 308 is a short action, while the 30-06 is a long action.
After that, there are 3 common bolt faces. One is small,223 for example), then you have medium,308/30-06) and then mag,300WM).
Anyway, the 308 bolt face is .473" in diameter. Just to give you an example, the 0.473" bolt face is used on the: 243, 25-06, 260, 270, 280, 7mm-08, 308, 30-06 and probably some more.
The interesting thing about every round I just rattled off ist he brass is one of 2 different sizes. One set is based off the 308 case, while the others are based on the 30-06. The reloading books all mention that a 243 is just a 308 case necked down to 6mm.
Anyway, your 243 is constrained to a short action, and ideally a 0.473" bolt face. This means your good options to change calibers are: 22-250, 243, 6mmBR, 260, 7mm-08,308, 30BR. There are probably some more options, but those came to my mind first. If you want to change the bolt face,which costs $$), you can do any short mag round,either WSM or SAUM).
Good luck! I'm still debating between all the above calibers except 22-250 and 243. My rifle also began as a 243.