Pawn shops will give you the least for your coins, but you might want to drop by one or local pawn shops simply to get a "starting point" of what your coins are worth. You mentioned that they aren't in great shape--whatever you do do NOT clean them. If they are only worth their melt value then the condition of the coins doesn't matter, but if they have collectible value (numismatics) then cleaning them will absolutely lower their value.
For both your stamps & coins, join subreddits like
https://www.reddit.com/r/stampcollecting/ &/or
https://www.reddit.com/r/numismatics/ , post pictures & you'll get reliable feedback regarding whether your stamps / coins have collectible value.
If your coins aren't worth enough to travel to get the best price, I think D&R Coin shop in Ocala (352) 817-6564 will offer you the best rates in this area--definitely more than any pawn shop.
If you have enough to make traveling worthwhile, check out Vermillion Enterprises in Tampa (352) 585-9772, or All American Gold & Silver Buyers in Apopka (407) 257-9944