FSI will train you for the type rating unless you are near dead, they just want the money.
If you don't have certain time and/or previous rating requirements set forth in the FAR you will have a limitation put on your license. This happened to me when I went for my initial Excel type. I had to fly 25 hours with a Captain before I could be let go as "unsupervised" PIC. Needless to say, after the 25 hours the company didn't let me be "unsupervised" PIC anyway with 2000 or so hours!
The least restrictive requirement to not have that restriction is 500 hours in any type ( the particular plane doesn't have to require a "type" rating, e.g. a king air 200 or 90 is fine) of turbine powered aircraft of the same category/class( might be making the cat./class up...go read the reg yourself). Or you have to already have a type rating in a Jet.
In a nutshell, as long as you can fake your way (meet the minimum requirements) through the checkride FSI will give you the type. From the information you have given you will have one of the two limitations applied to your type until you meet its' individual requirements....again, go look it up under FAR 61.
Now I need to go to bed!