It takes around 10 minutes by train from Venezia-Mestre to Venezia-Santa-Lucia (with about 5 trains per hour).
Bus service 15 runs frequently from the centre of Mestre to Piazzale Roma (which is as far as you can go by road when entering Venice). The journey takes around 15 minutes.
For reasonably priced accommodation, try this website:
http://www.hostelworld.com/
(Don't be put off by the word 'hostel' in the URL. Simply use the 'Additional search options' to select 'Guesthouses' and 'Budget hotels'. There are several promising hotels in Mestre, with good reviews).
Chris