What to do while riding?

Ok so I'm leasing this horse, today I went to ride for the first time alone (since I am leasing him from my coach she went the first few times to make sure I could handle him okay) and i trotted circles (I am really bad at it so I needed practice) and cantatas figure eights , and did a little no rein work controlling him with my legs... But it felt so unorganized like I didn't know what else to do... What are some fun things to do while riding alone? I am willing to try anything! Also hike half leasing a horse would it be bad to let someone else ride him or like 5 mins on a lunge line? My friend really wants to try him and I am buying him eventually and I trust this friend a lot , would this be a bad idea? Thanks!