Most Citation IIs don't have "FMS" per se - its normally a KLN90B or maybe a GNS-XLS. If you want WAAS in an early Citation II, you're probably going to be looking at a dual GNS 430W/530W install.
The V and Ultra still have JT15D engines, so their overhaul cost should be in the ballpark of 650-750k (similar to the C-II).
The CE500 is a very easy airplane to learn and fly - systems are simple and its forgiving. Being your first type, don't skimp on training - attend SimuFlite or FlightSafety, or SimCom at a very minimum for initial. I did my CE500 initial at SimCom MCO and was very pleased with it...but I had 3000 hours, over 1200 in jets, and 50 hours in type before I went.
You *will* have trouble getting insured with low flight time like that...especially if your owner wants more than $5-10M liability.
The underwriter will probably want 50-100 hours of "mentoring" before allowing you to act as PIC (you'll need 25 to get rid of the OE limitation on your new type anyway), and your "co-captain" simply isn't qualified to be PIC with 800 hours. They'll also probably want 6-month training for the first year.
You and your owner need to get insurance squared away NOW to prevent any nasty surprises in the coming months that could result in somebody losing their job due to inability to bind coverage.