I'm 5'9 and not plump. I ski a fairly high end stiff SL type ski in a 165 cm length, and a longer radius ski in a 190 cm length, I've tried out a few cross skis that make a compromose between SL and GS sized turns, and think a 170 length would suite me. However I believe I know how to use a ski. As you are a pseudo-beginner, you might want to start out on a 155 cm length in a short radius ski, or 165 cm in the longer radius ski.
Generally speaking, ski length these days goes from chin to a hand past top of head, depending on speed, size of turn, terrain and personal preference. Extra weight means extra length is required, but so long as you're skiing on groomed runs and not skiing at very high speeds you should still be okay without adding any extra length.
Another consideration is that since you are skiing hard snow and ice, and not soft snow you need a stiffer ski than you would require out west. Narrower skis are also more suited to the east ice than the west powder, and vise versa.
I would avoid any store that tried to sell you 145 cm skis.
The above is not likely to disputed by any knowledgeable skier, but this next bit is just my personal opinion. You should avoid "beginner skis" like the plague. You need a ski that will hold an edge and be able to turn you and reward you for making the correct moves. I would not go below an intermediate ski if I were you.
For $20 bucks you can get a subscription to a realskiers ( http://www.expertskier.com/
) reviews, which will categorize skis for you. Just make a short list of the skis and don't settle for one that does not include the "intermediate" (blue) skier Icon and good marks for clean carve. Quite a few of the skis reviewed have icons for beginner, intermediate, and expert all for the same ski. I would get one of those. The reviews go back a few years so you can find bargains if you want to recoup your $20.