Buying a bike gives you three options regarding mechanical issues:
1. You have enough money to not worry about learning how to fix/repair anything because you can afford to have someone else take care of it.
2. You do not have much money and are willing to research/ask questions about how to fix things or do basic maintenance on your own.
3. You do not have much money and don't care to learn and will stop riding when your bike stops running.
Not being good with mechanical things is something I have to overcome every time I pick up a tool!
It can be overcome with practice, a willingness to learn, and patience. YT is a great resource for learning everything from basic maintenance to very involved jobs.
As for which size bike, I'd lean towards a 250/300 (Ninja/R3/CBR group) just for the flexibility of being able to ride on faster roads as you gain experience. Used prices are not much, if any, more than what folks are asking for a Grom... at least in my area.