Neither one has horrible problems. Hell, even the lasers aren't bad on those. Honestly, the best I've seen. 20 years and most are running strong. They were tried and true lasers with no gimmicks of reading different color bottoms, GD-ROM nonsense, etc. They're solid.
I would go model 2 because they are easier to find. No other reason. I purposefully picked a model 2 Genny because it would be easier to find 32X cables, Sega CD, etc. Granted they all work on a model 1.... but I like the looks of the model 2 "tower of power" better.
Now the Model 1 tower of power with the Power Base in place of the 32x is just plain sexy.
Either one is good. For price, I would look at around 30. $35 is a good price. If you just want one to play today, I would expect somewhere around $50-$60.
For your first one, I would suggest going for a store or picking it up from someone reputable. They are solid. But they are 20 year old electronics, with moving parts, being shipped across the country... Solid or not, shit can go down.