Hmm... good questions. Depends on what equipment is available and how reliable. If your LDS is a little questionable on equipment, I'd go with the regulator since it's the most critical piece of "life support gear". I've seen a poorly maintained rental reg fall apart on a buddy, and though he handled taking a lung full of water exceptionally well, yikes.
If the rented gear is trustworthy, I'd recommend going with the wetsuit first, particularly since you're diving cold water like I do. Even good shops tend to rent wetsuits that are not wildly comfortable, and a perfect fit is essential to comfort and often warmth, since one that's too baggy doesn't work well at all.
I have a cold water wetsuit (J/J 7 mil) and a warm water wetsuit (3/2 full). Both were relatively inexpensive (under 200$) and both are exceptionally comfortable. My first wetsuit was a bought rental that was made out of aquaseal and hope, it was too tight, thus making it uncomfortable to dive in it, and so switching made a huge difference.
Second on comfort, I'd try out a few styles of BC and then determine what you like best. I started with a 50 dollar ancient scubapro BC which was quite functional, but not wildly comfortable. I'm not happy with being squeezed by gear AND as being female there are certain areas I really don't want gear squeezing, so when I tried out Dive Rite's Transpack wing system, I loved it and it's made a huge difference in my comfort level because I can have it full to bursting if I so choose with no discomfort. If the jacket style is your thing, again, finding one that fits you perfectly and has the features you want is going to increase your diving comfort.
Hope this helps!