Reckon I'll start with a medium sized axe and see how I get on. How much should I spend / any particular things to look out for in a good axe?
No! get a maul. It's the cheapest and most effective tool for splitting logs. axes and hatchets all have their place, but this is not the job they are designed to do. felling axes can get stuck and you'll do a mischief trying to get it free. I have over 30 years experience of this including on a commercial scale with a PTO processor, so I hope I've picked a little up along the way.
If you get a chainsaw expect to pay as much again on PPE; Boots, snaggy troos, helment and visor, check shirt.