I've had 2 LauraStar steamers. My current on is the Lift in Red. I'm not sure if it's the cheapest. You do have to depress a button to get steam. I'm not sure if that's what you mean by "depress for steam". I've never had an iron that you didn't have to press a button for steam. I wouldn't like it if it steamed all the time. I iron without steam more than with steam. I do love my LauraStar's. The first one lasted for over 10 years with daily use and lots of steam use as I was doing a lot of garments then.
I'm with you on the Oliso. It was cute and glitchy and lasted a year or so. I didn't even bother to talk to them about replacing it. I didn't want another one. I wasn't that impressed with it.