Be a bit careful. 4 is very young for a horse, he really needs an experienced rider to bring him on and work him through the wobbles he's going to have from now until he settles at about 6yo. I am not saying that you are not that rider, but think about it long and hard because if things go wrong you will both lose your confidence.
Am a bookoholic pixel and have shelf full of largely unused schooling books but this is one I regularly take out and read in the bath No you don't need massive arena lots of stuff you can do out hacking if needs be
If you are going to have lessons on him then i'd take pointers from those, i.e. have a weekly lesson then spend a couple of sessions practicing what you have learnt before the next lesson then hack inbetween. Just be careful not to over do it i.e. make sure you and the owner are schooling and having lessons on different days and keep up with the hacking. If you want to get started before the lessons then i'd start with rhythm - making sure he's walking and trotting nicely, working well into the corners of the arena, 20m circles, serpentines, figures of eight, lots of changes of direction, centre line, 3/4 line etc - keep his focus. Add in lots of transitions also. When happy with his walk and trot rhythm start adding in some canter. Don't let him plod around heavy on his forehand. Don't know if that helps or if it's a bit basic, it's hard to give advice without seeing you both, which is where the lessons will come in . Have fun
After a break of a few years, I've been offered a share! Now I'm overweight, unfit and very rusty, and he's only 4, but extremely chilled out and calm. He hacks out no problems and his owner is just starting to have lessons on him, which I've also said I feel I would benefit from, as it'll help my riding get back up to scratch, and mean we're singing from the same hymn sheet where he is concerned.
However, my memory of how I used to school is hazy, and I would appreciate any pointers! He's not been cantered in the school yet, as he's a big lad and quite unbalanced, so what's the best way forward with this? I feel like a novice just starting out, not an ex owner and regular competer! Lol