From a woman's perspective-
If you think you're going to ride a lot, and there's a chance of getting off trail and into fresh powder, a 340 or something small like that is going to do nothing but get stuck. Our first sleds were trail sleds- A Polaris 340, Polaris 550, Polaris 440 (race sled) and a Yamaha 500. They were all find on trail. They all SUCKED off trail.
Also- women particularly tend to want to start with something "their size". I was the same way, with both sleds and four wheelers. Fortunately for me, I had friends that informed me that I would QUICKLY outgrow the smaller stuff and recommended I get bigger equipment and learn on them. They were absolutely right. I ride a Yamaha 700 Grizzly four wheeler and will take it just about anywhere on or off trail. I bought a Skidoo Renegade 600 etec and wish I'd waited for the 800. The 600 has pep but my skillset now is such that I'd like the additional HP the 800 has.
So if you're going to stay on trail, what you've suggested and others have suggested will be fine, but if you're going to go off trail I'd suggest considering something bigger that is specifically set up for powder riding. Nothing will turn a new rider off faster than constantly being stuck. The newer sleds with the rider-forward chassis are also way better. You couldn't get me back on my old sled now, it's just night and day.