First, use a copy of the Guide Book of US Coins and categorize all the coins. Pay special attention to those in plastic holders from PCGS and NGC - the "grades" are likely to be reasonably accurate.
Second, list the graded coins and check their approximate values in the Guide Book. This will give you a rough idea of retail value.
Third, do the same for non-slabbed coins by comparing them to those already graded and, following the comments at the heading for each coin design, estimate the grade and value of each piece.
Fourth, many common coins, such as worn nickels and Lincoln cents, will likely be worth almost face value.
Fifth, silver and gold coins will be worth their bullion content at a minimum.
Once you've cataloged and estimated value, you can post coins here and ask members for input. This will help refine the scope and value of your coins. If the 1776 continental piece is an example, you might have many valuable pieces in the collection. [Coast to Coast Coin is an established coin dealer, although not known for handling especially rare items. The owner's name is Ken Pines.]