A serger is normally used in conjunction with a sewing machine.Having said that,let me ask you ,is the 30 year old machine still in working condition?? If so i'd take that in and get it serviced.Some of those older machines are better and more of a workhorse type than the newer machine.So if that's your case,then you will just have to buy a serger.BUT since you are new to sewing,i would buy it from a reputable dealer in your area,that way you get classes and have a support system if you should need it.

As for the stuffed animals i don't think you could do them with just a serger.There's all those little places you have to navigate around like the ears,paws etc and i don't think a serger would accomadate those very easily,nor do i think the seams would be strong enough to hold up under the use stuffed animals get.But that's just my opinion,and others may differ with it.
HTH
Kathi

I completely agree with both your suggestion about getting the older machine tuned-up and the statement that a serger is probably not good for making stuffed animals. Kathi. A serger is fantastic for many home dec projects. I made 4 pillowcases for a customer with my serger when I got home from work today. It is great for tablecloths, napkins, curtains, bedspreads, etc., but not so good for making stuffed animals.

A four thread serger gives you more options than a three thread model.