I'm looking to get my first brush and can't quite make up my mind between synthetic or badger hair.

Is it just a mild odor when held under the nose or will my whole bathroom stink like a wet dog the first few times I shave?

Synthetic shouldn't have a smell. I've owned a couple badger and neither of them smelled bad at all.

Now, boar...that's a whole 'nother story.

Neither should smell like that. Maybe it's the soap.

As was already mentioned, are you sure it isn't boar in your hand?

I haven't decided on what brush to get yet. For now I've been using DSC shave butter but I've always wondered what freshly whipped up lather in a bowl would be like.

Looks like I'll be staying away from boar then.

Not all boar brushes are funky.

Natural boar (especially Onega) tend to be the funkiest. Banded boar usually aren't that bad due to the bleaching/dying process used to create the band. This is an area in which Semogue excels.

With that said, I prefer the feel of natural boar. I don't like soft fluffy brushes. I want my brushes fairly stiff and somewhat scratchy.

My natural boar and badger brushes have all had a fairly off-putting smell when new.  Had to soap and rinse 'em a few times before I'd use them on my face.  I've never tried a synthetic brush that was worth half a shit compared to even a cheap but broken in van der hagen cheapo boar brush though.

The alpha shaving brushes work just as well as badger, but they are very spendy.  Probably going to give away or toss my Phoenix Artisan synthetic, since I got a second alpha to travel with.  It works okay now that I’ve got the hang of it, but it really tries hard to push all my lather to the outside of the brush instead of putting it where I want it to go.  Fighting with a brush to put lather where I want it is stupid and annoying.

I really only use synthetics because I travel a bunch.  Tried using a badger brush for travel, but it lathers inconsistently depending on water and soap available, and smells terrible if you don’t have time to let it dry before you put it up to fly.  And the one at home got kind of crusty and smelly after I didn’t use it for 2-3 months while traveling.  Overall I would recommend sticking to boar or badger if you don’t travel a bunch and for long periods of time.  A $10 boar or even low grade badger will do everything a $60 synthetic will.

Soak natural hair brushes in cold water, in the refrigerator for 72 hours.
wash with dawn dish soap before and after.

it speeds the breaking in period and gets rid of most of the smell (enough to use).

I have my badger brush for over 6 years now.  Rinse clean after use, shake off excess, hang brush side down to dry.  It smells vaguely of soap I use.

Don't overthink it.

Wash them with soap or Dawn. If using conventional soap, I rinse them in water with vinegar added, to help remove soap/mineral residue. Hang up to dry, and some instructions I read somewhere also suggested placing the brush in a sunny window for a few days.