I'm in exactly the same position as you. 
Might depend what your planning to do at the gym. If it's a lot of cardio on the running machine/cross trainer/step classes etc, what about 3/4 length leggings and either a lycra type running top or baggy t-shirt, whatever you're more comfortable with.
If you're doing yoga/tai chi etc then what about some yoga pants/jogging trousers and a comfortable sweat top to keep you warm.
If you're in the pool, I recommend a swimming costume lol
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You might find some good bargains at Sports Direct online (be sure to untick the box at the check out that takes an extra £1 off you for some magazine or something). I got some nice cheap sports wear to start me off from George at Asda (3/4 leggings and lyra t-shirt type top to match).
Top tip, only buy one or 2 'outfits' now, until you see what you're comfortable with, which exercise you're going to enjoy and stick to, and see what everyone else (doing that type of exercise) is wearing. If you see something you like that someone else is wearing, I wouldn't be afraid to compliment them and ask 'if it's not too cheeky, could I ask where you shop for your gym kit, it does look really nice?'
Good luck to us both for a fitter new year 