I want to add that if you've only had experience with leopard geckos, I certainly wouldn't recommend you purchase a basilisk.
I'm copying and pasting from
http://www.yearofthedragon.ca/bassie.pdf
Phylogeny: A member of the family Iguanidae.
Scientific name:Basiliscus plumifrons
Life Expectancy: 10-15 years.
Adult Cage Requirements: Tall vertical space (Approx. 5’) with a large water feature.
Natural Habits: Semi-arboreal and semi-aquatic. They enjoy spending time in shrubbery and trees as well as in the water and they are excellent swimmers. They can stay underwater for up to 30 minutes.
Diet: Insectivore, eating mostly small invertebrate prey items. A typical diet would be 10-12 appropriately sized crickets or the equivalent each day. Feeding of rodent prey should be rare if done at all. Supplementing the insect prey with calcium is absolutely essential. Sometimes these animals will eat vegetable matter but this is rare.
Heat: For the green basilisk the best way to provide heat is via an overhead heat source. They will benefit from a basking spot which reaches 35C (90F). The ambient temperature should be 26C (80F) to 30C (85F) with a cooler end that the basilisk can retreat to as low as 24C (75F) to 26C (80F). A thermal gradient is important to provide. As
long as it is not too cold for the human inhabitants of the house and there is no draft there is no need for extra heat
sources at night.
Water & Humidity: Basilisks will appreciate a large dish of water big enough to swim and submerge in. They will also enjoy being misted. Humidity is important for these animals because they come from a humid rainforest. It should ideally be 60-70% in the enclosure. This can be accomplished with misting, humidifiers, waterfalls or fountains.
And this is just the beginning... this is only one short caresheet. Apparently they don't tame down well and get stressed from handling.
I'd stick with the geckos.