FOR THE DIRTY HAT
Always brush your hat in an anti-clockwise direction.
We all know brushing keeps the dust away and a hat can collect dust for decades that can be pushed off with the whisk (felt is really resilient), yet for those more hearty deep down (the brush doesn't help) felt problems, I pull out my thick off white rubber hat sponge.
It takes out easy to get grease and salt stains (most from me handling the brim with my hands).
If that doesn't work I go heavy duty with Scout hat cleaner. Just spray it on and let it dry to a powder then brush it off.
If the stain is deeper and you are not used to using Naphtha or other cleaning agents, I suggest you take your hat to a professional. For Dress hats I highly recommend Graham Thompson of Optimo hats and Art Fawcett of Vintage Silhouettes
FOR THE WET HAT
Felt tends to stay in the shape that it dries.
If it is a soft felt hat like a fedora with a snap brim and the hat is soaked, leave the hat, brim turned up, on a flat surface with a towel underneath. If you leave the hat upside down on its crown (as many hatters suggest)you will end up with flat spots on the top of the crown. If you turn out the sweatband the brim will droop.
If it is a firm hat like a Western hat or like some of the Indiana Jones hats on the market, or a homburg, place a towel on the arm of a chair or a sofa and place the hat on the towell with the brim hanging over the sides. If you leave the hat on a flat surface the hat will conform to that surface.
FOR THE FIT OF A HAT
You want a hat that doesn't bind when worn... something you don't have to tug off your head as with time such a tight hat will cause headache. You also don't want the hat falling over your ears.
With modern hats, if you feel you are in between sizes it is better to go for the larger size. I know you may think you want a snug fit that won't blow away in a gust, though hat leathers tend to get tighter over time with the expansion from moisture then drying out constantly. Modern day felt shrinks.
More info on fit for those with marks on their heads.
Today, hatters don't make blocks for our specific heads. Back in the old days there were blocks for stars and they were custom yes... though that much custom is too costly (and questionably useful) for the time hatters have to make a modern hat., and when they sew in the sweat they tend to sew it in following where the felt lies. They do change the shape here and there to make the fit better... I have a German oval head (square forehead) with a bump on the right and I have had hatter corrct for that, though all in all if the felt isn't soft enough and the leather sweat is too stiff I'll feel it too much on my head. Alot of the difference is in the sweatband used. I prefer a rubber band feel. Kangaroo leather would be great though only a couple hatters use Kangaroo... not even Akubra uses roo.
In the end you may need to just wear the hat around and let the band soak in some sweat and let the leather break in. And if that doesn't work go a hare bigger in size.
FOR HAT QUALITY
Most vintage dress hats are far better in quality than those you can have made by the the best hatters on the modern market.
Resilience to rain is one of the most important factors. Your felt hat will soak through in a downpour... felt acts like a sponge. The determiner of quality comes from how much the hat can take the rain without drooping over time.
With soft hats like fedora or homburgs, pliability and the ability to take being crushed and rumpled and squeezed is a determiner of a soft hat's quality. Can the hat be crushed or rolled and return to it's original shape without the integrity being compromised. No hat can take constant rolling and crushing, just like no dollar bill can last forever under the constant folding and crushing. Some papers as some felts are better than others. I don't recommend rolling your hats for travel, though it is something I have done.