Remember though, if you go custom you are not going to be able to play your guitar before buying it. If you're in the position (and you are) where you don't even know what style of guitar you want yet, then buying a custom might be a bad choice: you simply won't know if you like the style of guitar that you'll end up with.
Just go to stores and play some instruments first, find style of guitar you like (i.e. thickness of neck, radius of fretboard, size of frets, variety of pickup). Then, if you really crave a custom, custom order a guitar with the specifications you found you preferred in the store.
Edit: You should also buy a guitar to suit the course. In my experience, Strat style guitars are by far the most flexible, and in addition you're likely to spend most of the course playing funk or jazz based music (simply because that's what the majority of guitar session work consists of, and these courses tend to be session-focused). A degree of intensive guitar will also mean the guitar will be used heavily, so make sure you'd be happy with whatever guitar you buy accumulating a few knocks and dings along the way.
As someone who's just finished a year long accelerated guitar course, you will not want that Les Paul. They're absolutely wonderful for rock, but I'd run out of fingers to count the number of times I had to borrow a Strat from a friend because the Gibson wasn't appropriate.
