Sadly, there's no real cheap way to "try" Universal. It usually works about the same whether you buy a 2 day ticket, 4 day ticket, 5 day ticket, or season pass because Universal runs buy 2 days get 2 or 3 free deals all the time, and these tickets are usually only about $50 less than a season pass.
However, the cheapest ticket is a one day no hopping ticket. You never see discounts for these, though. The buy 2 get X free is the main deal Universal offers. The next cheapest would be a 2 park no hopping ticket. Note, with this ticket, you cannot ride the Hogwarts Express between parks.
The cheapest places I have seen to purchase tickets from are Undercover Tourist, Triple A South (if you are in a southern state), and Costco. You just have to compare prices to see which is the best deal. It's usually Undercover Tourist but not always.
Something else to keep in mind is that you can always upgrade tickets. You can do so at Guest Relations and certain kiosks in the parks. This means you can purchase the cheapest ticket and then decide day of if it's worth paying the price difference to upgrade it or not.
As far as onsite verses off-site hotels. It really depends on what you are looking for. Universal has some great deals on their resorts, especially if you have a season pass and can get the AP discount or if you are ok with staying at one of their value locations that are located off-property. I've also had luck with renting condos for very good prices from Vista Cay which is super close to the parks.
If expense is the number one factor, look at the two offsite properties (Surfside Inn and Suites & Dockside Inn and Suites). These two consistently have the lowest prices. They offer free bus transportation to the parks which is reliable and fast (only about a 10 to 15 minute ride). The properties are nice and clean, so you know you're not getting a roach motel.
If you are thinking of purchasing Express Passes, you may want to look at staying at a Universal premier resort instead. These resorts are very expensive, but they give EP to everyone in the room for the length of your stay starting at park opening on your check in day and going through park closing of your check out day. Considering that EP can run up to a couple hundred per person per day, staying at a premier resort can be worth the extra expense on the room. Many people book what is called a throw-a-way room where they book one night at a premier resort for the 2 days of EP that gives them, but don't actually sleep there. They stay at a cheaper resort or somewhere cheaper off-property. Some people do split stays. This is the one big way you can say a ton of money if you were planning to buy EP.