I don't know too much about Pilates except that dancers were doing Pilates many decades before it became popular.  I'm also not sure how difficult it is if you're totally out of shape, i.e., what kind of help they give you if you can't do the stretches.  I would imagine it's like yoga, where, if you have a good teacher who understands your limitations, they can guide you gently through each session so that you only do what your body is capable of.

 

Re: the swimming ... I also would have to first buy a bathing suit!  And when you get fat, it's a big shock to see the sizes you have to buy.  Speedo usually isn't good for when you get fat; I always found them too tight and too risque, so to speak!  You don't want your ass hanging out.  lol.  I can't remember the brand I used to buy, but they had good racing swimsuits that held everything in and went up to sizes 36+ beyond.  I bet anything that there will be plenty of fat ladies at the swim classes because that's the kind of exercise that overweight people, people who haven't exercised in a while and people with arthritis tend to be able to do.  It's easy on the bones and great for toning.  Swimming doesn't help you lose weight, as some people think, unless you're swimming laps 5 and 6 times a week (and even then I didn't lose weight!!), but swimming can start to tone-up the flabbiness.

 

I think the Pilates and/or the swimming is probably best for you but if you can get a good deal on that machine and if you still think you'd prefer a more vigorous workout that you can do out of the eye of the public, then go for it!  It's a great price.