You can get to Lake garda by train if you do not wish t hire. The main line from Venice to Milan goes through Peschiera and Desenzano on th southern shorres of the Lake. There is a competentferry service to take you round the lake from these two towns.
For car hire the major rental firms have offices at Piazzale Roma in Venice - as far as cars are allowed into Venice. Avis are 496G, Piazzale Roma (www.avisautonoleggio.it); Europcar are at 496H Piazzale Roma (www.europcar.it); Hertz are at 496F, Piazzale Roma (www.hertz.it)
Check with you own car insurance in UK - they may cover you in Europe, a few do. Your UK car driving licence should cover you as a visitor in a EU country. You may well be asked to leave your credit card number as security for damage and pertol to fill the tank at the end of the hire period. Check the car you actually get is the one you agreed to hire as it is all too easy for them to be out of a particular car whe you arrive to pick it up - if they upgrade you free of charge fine.
I have hired cars in italy on several occasions and it has always seemed a straightforward and well organised procedure.