Certainly, it's good to want to get in there and get working. But do you know if the wall you want to remove is a load-bearing wall? You need to find this out. It might be worth getting a bid or 3 for the job, and ask each and every contractor if the wall they remove is load bearing. Sometimes, you can get away with finding out yourself by seeing if there's a header in there. But that may not be enough for the 'untrained eye'. Be careful w/this because you'll have a hard time explaining to the insurance company why the 2nd floor is now on the 1st floor ...
In all honesty, I'm not going to tell you if you should or shouldn't get a permit. If your municipality requires it, some contractors get them, some don't. It really DEPENDS on why the municipality wants a permit. Maybe, if you're just removing a non-load-bearing wall, you don't need one. BUT, if you're installing new electrical work as part of the job, perhaps you need one. See what I'm saying??? Ask your contractor is a permit is part of his 'fee'. Then, ask why a permit is needed, (or why not.)
As far as what your finished job will do to the value of your home is hard to say. My house, believe it or not, had the master bedroom 'reduced' to create a, somewhat odd shaped, 10' x 9' x 12' bedroom. Sure, 4 bedrooms in my neighborhood adds value (in spite of the shape), but 80% of the other homes still have 3 bedrooms. Certainly, the POTENTIAL of having an additional bedroom MAY add value to the home but if you REMOVE a bedroom, I can't say. I guess the only way I could safely answer your question is to see 'who is buying your house'? If the potential buyer (PB) is a young couple w/no kids, and you end up with a 3 bedroom house, I think you're fine. BUT, if you have 4 bedrooms and a PB that has 4 kids might want the 4 bedrooms. In short, you've 'cut out' potential buyers (when you cut out your wall.) It's tough to say, I guess, in any scenario.
Now, as far as county assessment goes, you may or may not reduce the assessed value of your house by 'removing' a bedroom. THen again, you may not. If the value does drop, it may be minimal. I don't know if I'd go asking around because you may raise some eyebrows, unnecessarily. There's no law that I'm aware of that requires you to tell the county you have 1 less bedroom. Just wait until the reassess your home to see what 'they say'. You can go to the municipal office and get a copy of the 'sheet' that shows the assessed value of the other homes on your street, and you can compare them to yours. (Don't tell your neighbors because they may feel their privacy is invaded.) I'm assuming there are similiar homes on your street. If you know your neighbor has 1 more bedroom than you, and you both, basically, have the same house (otherwise), then see how their home value compares to yours. Oh, the Assessed Value for your home is for TAX purposes ONLY. It's NOT meant to indicate the Market Value or Appraised Value of your home. (They're all different values for DIFFERENT purposes.)
Maybe others have more to say. My best to ya and hope this helps.
PS: After this afternoon, I'm out until MOnday morning ...