The first thing I'd say is that your tires have waaay too much tread on them so you'll need to fix that (read: Ride it a lot!)

As for upgrades...I'd say while you're fixing your excess tread problem, make notes of things that you'd like to change, e.g. seat comfort, how well it shifts, etc... and go from there.

As for pedals, go ahead and get what works for you, knowing that you don't necessarily need to be clipped in in order to ride. There are positive and negative arguments for the entire plethora of options of shoes and pedals, to wit: http://www.bikeforums.net/archive/index.php/t-181397.html and http://www.bikeforums.net/archive/index.php/t-610366.html

Other things to think about: Lights (front and rear) if you're going to be riding at night, racks and panniers (saddle bags) if you're going to use the bike for commuting and errands and such.

A good informational resource for cycling and it's various aspects, we bow down to Sheldon Brown

So, welcome, but be forewarned. When I got back into bicycling a year ago, I had one bike; now I have five.

Enjoy...

...and go fix that tread problem!