Asbesto's is a pain and not DIY friendly at all. I don't mind doing small projects exposed to it because limited exposure is relatively safe, but as much as you have should have some real remediation.
Depending on your town, I'd suggest going to Lowe's or Home Depot for the different projects. Those guys know enough to help and are customer oriented. The guys at specialty houses (plumbing supply or electrician supply) are more knowledgable but tend to be snobs when working with lowly DIY learners.
Plumbing is very DIY friendly these days with PEX and PVC. Hardest part of the bathroom will be lining up the tub and drywalling around it. Electrical is different, I do my own work at the plug side and change a breaker or two out but for a full panel I'd hire a pro. Getting that wrong is a very bad day. Overall the other projects are just smaller things you learn as you go. You'll become friends with the folks at the stores you go to alot, I used to know the plumbing and flooring peoples kids names when I was first rehabbing housesl.