I just used a specificly new washing tub in the kitchen sink, baby bath was used once as i pulled a muscle transfering it to the table, i won't be getting another one this time.
Nursing pillow? well i would just get a triangular pillow which is useful to use as a napping pillow downstairs, although the proper nursing pillows sell really well on ebay, so you could get most of your money back doing that.
Baby gym/play mat, yes these are great from the start, you can also use the triangular pillow on these for tummy time, and put a towel underneath them on it for some nappy free time if they get a rash.
i wouldn't bother with a cot mobile really, they never really keep baby in the cot longer than when they want to get out and see you, eat iykwim.
Night light, well if you think long term them they can be worth it, my ds is 4 and has had one in his room since birth, handy for feeding/changing at night without too much disruption, and used when they are toddlers when they hate the dark, or when they learn to get up and go to the toilet at night.
You can get most of these cheap on ebay or second hand/freecycle etc, so doesn't have to be a massive outlay.
Babies don't need fancy things, if anything the simpler the better.