I think you're in good shape. Jalapeños are basically the gateway drug of gardening because they're so easy to sprout
as long as your pots have drainage holes and your soil isn't super heavy or chunky, they’ll pop just fine
my secret is probably heat, if your house is chilly, try putting the pots on top of the fridge or near a warm window.
I don't think you should waste money on fancy gear yet, though