Can a layperson dare to handle the baseboards themselves?

We nailed the moldings and mitered the corners. It was quite easy with a measuring stick, pencil, nail gun, and miter saw with angle adjustment. I didn’t want to glue on clay plaster, so I nailed instead. Both methods work equally well.
Start at one spot and always measure the next piece. You don’t need to do much calculation.
Corner blocks make the miter cut unnecessary and thus simplify the installation. But I don’t think they look as good. You only catch on them if the blocks are thicker than the moldings and create a protrusion.
Your thoughts are correct, just start in the least important room. It will work out.

Exactly. I would buy an electric miter saw that you can use around the house from time to time. If an angle isn’t quite right, you can finely trim it. Eventually, that will even be fun and motivate you to work on more projects, maybe even in the garden later.
Possibly, I would choose smooth surfaces, so without decorative profiles. If you have many moldings, you could also consider having MDF strips cut from the board according to your own wishes, having the top edge milled/rounded, or something similar, then painting the moldings yourself as you like and nailing them to the wall. You can do all of that easily yourself, it costs less, and it can be fun.... maybe. We once sprayed moldings, etc. with leaf gold from a can..... MDF makes it possible to try something different every now and then.
Gluing wouldn’t be my thing either, but I suppose you can do that as well.

Mainly glueing because clipping is too cumbersome for me and I don't want the holes/nails to be visible on the moldings. We have wallpaper underneath anyway, so I don't have many worries about glueing them. There are special adhesives for that, in a pinch hot glue would probably suffice, what could really go wrong with that.

I will definitely go shopping and probably start over the weekend, you are absolutely right. Just get started. It can't look worse afterwards than it does now. :) I actually find mitered corners prettier than with towers, I was just a bit intimidated by cutting.

edit: Oh yes, is there a basic formula for approximately how many meters of molding you need?

There are special adhesives for that, in a pinch hot glue would probably also suffice, what could possibly go wrong with that.

Just helped out the neighbor last weekend. 20€ hot glue gun from the hardware store, a few sticks of glue, acrylic, and a cartridge press... Looks great. We started in the storage room and then did the rooms that need bigger pieces first. See below.

I actually find miter joints prettier than with little towers, I just was hesitant about cutting.

It's just fiddly stuff. If it doesn't fit at all, you just take a new molding and use the other one somewhere else. That's why we started with rooms where you need long moldings. We messed up the cuts several times but were still able to use those pieces elsewhere, so our waste was minimal in the end.

edit: Oh yes, is there a basic formula for roughly how many meters of molding you need?

We measured everything roughly and then took 10m extra. We had to use one extra molding. We'll return the other 8m if Corona allows.

We have white baseboards. They were glued by me and my brother. We cut the miters; where it wasn't so precise, the white acrylic conceals it. We used the cartridge adhesive from Hagebau as glue. Since it wasn't enough, we simply continued with sanitary silicone. Everything has held until today, since August 2017.

edit: Oh yes, is there a basic formula for approximately how many meters of moldings you need?

What do you mean? You measure how many meters your room has all around. Also consider that you might need a few extra meters so that in the end it doesn’t get too fragmented, for example due to heating pipes, doors, projections, etc.

Just start first. With straight walls, miter cutting is no problem; the more crooked the construction, the more skill is required. I find the external and internal corners quite nice, but yes, they often don’t last forever and collect dirt. Better without, especially since they are also expensive.