I have a Grizzly 7x12 mini lathe, which is just a repainted Sieg C2 lathe. If you're not looking for super accuracy you can start working with it right out of the box. It's biggest drawback is lack of a carriage lock. Locking the half huts helps, but there's still a lot of play, and it will adversely affect any facing or parting operations. I think one of the first things to do is add one. There are plenty of designs out there, but I think the best ones clamp the carriage down onto the ways.
The one I made bolts to the mounting holes for the follower rest on the left of the carriage. You can't see it, but the center socket cap screw threads into a T shaped piece which rides under the ways. Aside from the screw there is also a locating pin between the two pieces to keep it from spinning when tightening or loosening. One half turn of the screw goes from free to locked. If it gets too annoying on the left of the carriage I'll drill and thread holes to move it to the right, but I hate threading so it'll need to get fairly annoying. You can also see the added way protector, which is just the bellows ways cover from a X2 mini mill cut to size.
UPDATE: I added a lever to make locking it easier. I also glued a magnet in place to hold the lever in place and accessible until needed.