Julian,
Many have replied with sound advice and to add to the list I'll say: go to someones shop and try every plane you can! Spending less than $40 on your first plane is meaningless if it doesn't work and the only way to know how good a handplane can work is to use a well fettled one.
I have both old and new in my shop and had I tried a new plane first I might not have spent so much time tuning old planes. That being said, taking an old plane and making it sing is truly sweet! And acquiring the skills to tune an old one will serve you well. If you do go the old route I'd suggest a new blade. And regardless of the planes you end up with the first step is learning to sharpen.
And lastly: fasten your seatbelt cause handplanes are a slippery slope!!
Oh, one more suggestion----get or make a good bench, handplanes need a solid work surface!