A basic OBD reader costs pennies from eBay, either to connect to your laptop or a standalone version. Beware of Bluetooth though, if the connection drops half way through a scan you can cause a lot of problems.
When you want the proper diagnostics beyond the basic engine stuff then you're into a lot more expenditure, something like a Launch X-431 is entry level and still into four figures once you've got the subscription sorted. As Gavin says one machine won't do everything you need, so most workshops use several machines plus VAG-Com and potentially some other laptop based solutions too.
In your situation I'd get a USB OBD-II connector and have a play with some of the software that's available online, that way you can do the basic stuff like clearing codes and reading the cause of a MIL light on most cars, but you're not spending a fortune. It's not worth going any deeper than that, because you need to be able to interpret the codes to get an accurate diagnosis anyway, and that is a black art all of its own!