How do you choose craftsmen or obtain multiple offers?

I would always choose the one who takes the trouble to come on site and write a good offer for you. Offers from a distance are worthless. It always gets more expensive

If you have a neatly structured offer, you can take out the text modules and forward them to other companies. Important, prior telephone contact and coordination. Either they come themselves promptly and measure/calculate themselves, do not come and use your template, or have no interest.

Pure email inquiries fizzle out…

How do you handle it when you choose a craftsman or do you request multiple offers?

Here are our criteria - not all can always be met 1. Local near the construction site 2. Committed to the community -> values his good reputation and is locally recommended. 3. Obviously enjoys his job very much. Loves his trade. 4. Maintains good manners with employees, positive company culture. 5. Speaks plainly 6. Interested in my project and not just the money it brings 7. Likeability I am willing to pay for quality. I only verify the offer’s plausibility if the craftsman If he is then a bit more expensive, that’s OK.

Is interested in my project and not just the money it brings

Yes, I think that is also very important. That was what I liked about the all-rounder. He doesn't see it as limited, for example, to the floors, but as a whole. That's why, for example, also the doors or the yellowed sockets that he wants to redo/clean.
I'm curious about the final offer. What bothered me was that it kept getting more expensive since the first conversation. That's why I now have an on-site appointment with another floor installer/painter, at least to have a comparison and not be dependent on just one craftsman in the end.

What bothered me was that it got more expensive with each conversation since the first one.

Address him about this impression and express concern about your budget.
There are more reasons than profit optimization why such projects become more expensive from one conversation to the next. For example, because new aspects are added that were previously unclear or because the client's wishes change—explicitly or implicitly.
Investigate the mechanism and decide according to your assessment of the mechanism behind it.