Cats and reptiles do not mix, especially a small gecko like a leo (9"-10 1/2" average). The cat(s) can and will easily kill this relatively slow moving lizard.
The cage is a must, for the gecko's health and safety. They actually feel secure in their homes, so it's not cruel.
Basic needs for an adult leo, is a 20 gallon long (29gal regular or 30 gal regular would work too). This offers plenty of floor space for the required hides. Around $30-$40, a strong screen lid is a must
Under tank heater -$15-20. Leopard geckos are nocturnal and in the wild would use the day warm ground and rocks to digest their food after the sun went down.
3 Hides, you can buy them or you can make them. You need a warm dry hide, a cool dry hide, and a warm moist hide (tupperware container with a hole in the side, lined with damp papertowel).
Substrate can be paper towel, reptile carpet, or texture ceramic tiles. Loose sand is a bad idea, as leos can get easily impacted, likewise the stuff like bed'a'beast can impact them and also make their cage too high in humidity.
Digital thermometer with probe. Petsmart sells little ESU brand ones for $8-10.
Water and food dishes. Again, you can buy or use something around the house. (One of my leos currently has a peanut butter lid as a water dish
Food must be live insects. They cannot survive on freeze dried or any of those roasted can'O whatever. They are drawn to live moving food. Average is 10-15 mealworms every other day, or 8-10 large crickets every other day. Depending on where you buy these, it can get a bit pricey. You will also need gut load for the insects - this can be bought at petstores - and containers to keep them in (at least for the crickets).
The gecko's warm side must be between the 88F-92F, any higher or lower and it will be unable to digest or avoid that side. You can keep the temperatures at range with a thermostat. A simple one can be bought for around $36 online or at petsmart.
I think I covered most of it, probably a bit out of order
If you have anymore questions about them or any other geckos, just ask.
Or you can register here and ask http://www.reptilerooms.com/PNphpBB2+main.html
The Leo section there is probably the best of any reptile forums I've came across.
Oh! and it's wonderful that you're considering adopting a reptile. Leos alone have a rather long life span, into their 30s with good care, so there's always some out there that need new homes.