Welcome! There is a
very good sub-section of this board that discusses storage and conservation issues in detail, you may find it helpful.
Generally speaking, sellers/dealers usually keep coins in
flips that are flexible and durable so that they can be handledat shows and travel in the mail, but they are usually not ideal for long-term storage. (There are detailed reasons in various posts in the Storage section). You probably will want to switch those coins to archival
flips. Our host,
Forum Ancient Coins, is one of the few dealers that ship coins in archival
flips that do not need to be replaced and I believe sells archival
flips, too.
As to coin trays, it is mostly up to you. A lot of collectors seem to keep the coins both in
flips and in the trays, and some trays are sized for that purpose. If you have those trays, you might prefer to keep them in the
flips. The biggest problem with trays is "gravity" -- dropping a tray of loose coins is not fun. However, coins do look much nicer on display "naked" in trays and perhaps you can balance them well. There are discussions about trays in the Storage sub-board.
Also, check the tray manufacturer's information about the material used to line the trays. Some trays may be more chemically active than others.
Enjoy!
