How much should this home repair cost, and who should do it?

Some of the wood that supports my gutters is rotting. The larger wood isn’t so bad, and can just be painted, but the thinner wood, right below the gutters, needs to be replaced, all around the house. Except on the right side, everything (all wood and gutters) needs to be replaced.

Can they replace the wood without replacing the gutters? Except for the right side, the gutters are in good shape.

And would a typical gutter company do the wood as well, or will I need someone else to do it? A roofer, maybe?

I have never had any work like this done, and I really don’t want to get ripped off.

The arrows point at what I’d call a barge board. The barge board supports the gutter. So the gutters need to come off to replace it.

I’m not familiar with US gutter systems so can’t advise you on how easy or hard yours are remove.

In NA, that is called facia board. The gutters are fastened to it, as dynamitedave says.
Get several estimates.

Hire a general contractor to replace the wood, paint it and put up the gutters. You can hire separate contractors to do the work if you like, You’ll be lucky if they don’t find more damage from the water problem. Saving small sections of slightly damaged wood could cost you more in labor so remember not to have them saving and splicing in everyplace there is a transition between rotted and solid wood. Every splice is a potential rot start point too.

I agree with Harmonious Discord - be prepared to find more damage than what is readily apparent. Basic aluminum gutters really aren’t that pricey; depending on length you might be better off replacing them.

I called a gutter company for replacement of the rotted edges of our roof and new gutter hanging (we had very old “box” gutters that had rotted completely away). The first estimate was $20,000. Which is ridiculous.

The next two companies came out and looked failed to ever respond with an estimate.
Other gutter companies only hung gutters, they couldn’t do the necessary carpentry work.

I found a guy (general contractor) through word of mouth (personal recommendations are gold) who did the job for $3000. In most places the entire eaves of my roof had to be rebuilt and reshingled because of the damage. They tore off the old material, rebuilt where necessary, hung new soffit and fascia and new gutters. I ran around the house admiring them in the next rain storm.