Where/what wet vac to rent?

Provided you are local to that hirehere.ie place, 25 quid a day to rent a wet vac machine is quite good....provided you get small attachments. They might only provide a large attachment for doing large carpeted areas. Collect it first thing, and go over the car twice with it, as often when the seats dry out from the first attempt, it can leave a tide line from the area from dry-wet. So if you were willing to do a full day with it, doing the carpet, seats, matts it would be worth it.

Given you've said they are light stains, Id try something like Chemical Guys Fabric Clean - diluted down 1 part to 5 parts water, I found it quite good. Spray on, scrub with a nail brush, wipe off with a microfibre cloth. First attempt will usually do it, but if it was something like milk or yogurt if its from kids, repeat two or three times, it should do the job!

Another option
Lidl are doing a 1400w wet vac for under €60

You'll have to spray the cloth with a bottle full of cleaner first