Get a Mazzer Mini or Super Jolly used on eBay for <$300. They are indestructible so used is fine.
Gaggia Classic is probably cheapest entry-level machine (it's what I have). Steaming sucks though. There is some mod you can do to add a Rancilio steam wand that apparently makes it better, but you'll still have single boiler issues, unavoidable.
Otherwise Rancilio Silvia is a good bet.
Or start saving for that double boiler.