Definitely do the direct access if I were you. I did an intensive 3.5 days and test on the 4th. It’s awesome and you can have as much fun on a £2k motorbike as you can in a £50k car. I still remember getting on a brand new fireblade in 2008 and just couldn’t believe something so much fun was still legal.
Why not get a 125 for now? If you buy right it’ll barely cost you a penny and you can get some practice and road skills in advance of your test.
So many bikes to choose from these days, but the advice I wish I had followed was just buy the bike you want. If you make compromises on the way like buying something you feel you should (or other people feel you should) you’ll still get to the one you really want, but you’ll just lose a chunk of money on the others on the way
Enjoy it. It’s one of the best things I ever did.