Hello!
There shoudn't be too many national differences left between JAR states, however take my words below with caution and ask your CAA if in doubt. This is how it works here:
You can not unfreeze your frozen ATPL simply by getting type rated on a multi-pilot aircraft. To unfreeze, you need 1.500 hours total time, of which 500 must have been flown on multi-pilot aircraft. So even with an MPA type rating in your license, you will have to fly the thing for 500 hours before you will be given your full ATPL.
Every part 25 certicied aircraft is a multi pilot aircraft. Most part 23 certified aeroplanes are not multi pilot aircraft. There are a few exceptions, though: Hours flown on so called "commuters" count towards your 500 multi-crew hours. Our aviation authority (LBA) has a downlodable list of types that qualify as commuters. Your CAA should have something similar. On "our" list, you will find types like the Metroliner (SA226/227), Dornier Do228 and Beech 1900. All of them fairly complex 19-seaters with not much automation (or none at all). I have flown some of my 500 hours on the Metroliner myself.
Coming back to your question, the cheapest type rating will be on one of the types on this list of commuters. But honestly, I would not recommend it. Spend a little more money and get rated on a real part 25 aircraft. You will get paid decent money starting with the first hour (show me a Metroliner operator who pays his pilots well...) and will recover the extra cost quickly. Depending on your career planning - airline or business aviation - the lower-end typeratings (cost-wise) will be either small turboprop airliners (Dornier Do 328, Saab 340, ATR 42 or Embraer TPs) or small part 25 bizjets (Citation 500/550/560, or one of the smaller Learjets). But please, only pay for your own type rating after having signed a working contract with your future empoyer!
Happy landings, Max