With computers, my advice is to select something that will suit you for our future diving. At present, I own a Heinrichs Weikamp OSTC2n and a Suunto Vyper Air. The OSTC2n is an OLED screen all-singing all-dancing techie thing and the Vyper Air is a typical wrist mounted affair.
I bought the Suunto first, after hearing plenty of good recommendations. At the time, I was certain I would never go down the techie route. I ended up doing more ving in the deeper recreational range, and found I was getting close to deco. Then the twinset came and I started doing deco diving.
I found I had made the right choice with the Vyper Air, as the lower models did not allow nitrox above 40%, or gas switching, which comes in handy for accelerated deco (switching to a rich nitrox mix when decompressing). As I got even more adventurous, the OSTC 2n came. One the features of the Vyper Air is 'gauge mode', which means it does not give deco information - just run time, average depth, max depth. and current depth (so it acts as a 'bottom timer'. On adventurous dives, I'll have a plan written on a slate, which I can track using the Suunto. I'll mainly be following the deco plan on the OST 2n, but if that fails, I have the plan as a backup. When I bought the Suunto, I didn't have this in mind, but by luck, I made the right choice.
For a novice, that last paragraph may not make sense, but my advice is as follows; if you are 100% sure you will never go beyond recreational limits, most computers are going to be okay. Make sure you get one that is compatible with nitrox (I think you'll have a struggle to find one that isn't). I chose Suunto because they are popular here I dive; this is useful as it means you are more likely to be using the same algorithm as your buddy. If there is a possibility you'll go down the techie route one day, look for one which works with nitrox up to100%, allows gas switching and has gauge mode; you will never grow out of it then.
For fins, this is very much a case of personal choice. If you can, try and have a go of a few pairs - what works well for some, may not for others. Personally I like basic, stiff fins and have a pair of Scubapro Jets I dislike splits and anything gimmicky. Some like splits and say finning feels effortless, but they can be a it tricky when you need to get some power in your kick.