Last time I went (by car) to Reading station, you could go in to the car park at the SE corner of the station and stay free for a short stay (can't remember if that was 20 or 30 minutes) - signs said you had to get a ticket from one of the machines (to prove what time you parked) and I think you were only allowed to park within one area of the car park.
Obviously there is a chance it has changed since then - this was a few months ago.
Also if you're not used to Reading town centre, be aware that there are frequent changes to the road layout near the station, and that there are a lot of bus / taxi only roads / lanes round there.