You've gotten a lot of good ideas and ones that most RVers use.
Just roam the plastic storage aisle at WalMart for containers to hold things. Buy an assortment as see what works. Return what doesn't.
For dishes - we've used Corelle for 16 years of full-timing without any breakage - we found in the home goods dept a tiered dish holder made to fit in a corner. I put the Corelle on the bottom tier, and paper plates on the above tiers. I don't separate the Corelle with any protection. Cups and glasses ride just fine as is if they don't have a lot of space between.
If you find that you're not filling up the cabinets which doesn't happen when full-timing :), then take some rolls of paper towels or toilet paper and use them as separators.
Finally, make sure your cabinets and drawers have a good closure mechanism. If they're loose, use a small bungee between two cabinet door handles. For a stack of lower drawers, weave a yardstick down through the handles. Doors flying open during travel are the main culprits of breakage.
Enjoy your new RV!