Different sizes? What are you referring too?
There is different OD between manufacturers and even between styles, but generally tyres of the same range are the same size. ie: for example, a Ride Re(LT) inserts is the same size in either 28, 32 or 36 compound; however, a Rex30 or 34 is slightly smaller OD (not much, about 1mm) as it is a squared off profile.
Offset changes where the rim "width" sits with respect to the hub mounting point and can alter your cars track width. In absolute terms it is a measurement of how far *offset* the mounting point of the rim is from the centre of the wheel.
2mm positive offset wheels will sit further "in" under the body and reduce the track by 4mm overall. This is as the mounting point of wheel is 2mm further "out" from the hub, dragging the rim further in. 4mm on 190mm is quite a big change. Narrower track will be less stable and twitchy in comparison.
You can look at a calculator here for full size tyres - it will explain it quite well I think. http://www.1010tires.com/Tools/Wheel-Offset-Calculator
As for tyres, I assume being a car park you're looking at a low grip scenario, so look towards tyres that are tagged for low grip/carpet like the Ride Rex30 or their RE with LT inserts - or whatever the guys that are fast are using!