Just bought a used rider...first snapper

So I had been looking for a snapper rider for several months as I am tired of pushing a mower around on my 1/4 acre lot...just takes too long, plus I am 72 and a little more tired. Most folks were asking 5-700 for a well used rider, mostly the 28" version...but I happened to find one advertised for $125 ( yeah too good to be true) It is also a 33 inch version, model 1333, from about 1995. I called not expecting much, but the fellow said it runs and cuts, just needs a new battery, but starts on the second pull. Got there and , sure enough, the mower works! Doesn't look too bad either ...the guy said, heck you can have it for a hundred...so I load it on my trailer and take it home...was able to mow the lawn that day, but I don't lke pull start and the motor kind of runs a little rough...so I get a replacement carb on amazon for 20 bucks and a new battery at advance auto..put it all together and this thing starts better than my new car and runs real smooth now. Now for the bad news....my lawn is not perfectly flat, but really not hilly...but when I ride on a slight incline sideways, I feel like I am going to fall off! The rear section seems to tilt independently from the front and I am feeling quite insecure on this thing. I put some side bolsters on the seat out of plywood and , at least that holds me in a little, but I still feel very uncomfortable. Is this normal with this kind of machine? It definitely is a little of a beast...but it certainly has plenty of power...I have not tried going past 3rd gear yet...as it feels like a race car.