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Go straight for a 7x7 and 4-6 will be pretty easy to solve once you're done with 7.It's difficult to say... everyone has their own personal preferences. Can't you buy all the puzzles now, and try each for a day or two, and decide an order for yourself?
Otherwise, I would suggest the natural progression is to bigcubes first, and other twisty puzzles later.
13x13 isn't WCAI am a traditionalist, and will probably only do 3x3.
Something like the 13x13 just seems crazy to me.
13x13 isn't WCA
Go straight for a 7x7 and 4-6 will be pretty easy to solve once you're done with 7.