My DD is 7 weeks (my first) and the things that have been useful for us:
Moses basket - she sleeps next to our bed in it every night. In retrospect I would have bought one of those little cribs which have slatted sides so I can see what she's up to (and she can see us) but it's been fine and the rocking stand we got it has been a godsend as she's quite colicky in the evenings. Get a plain one, I spent ages selecting between designs and then you can't use the quilt anyway so they're all pretty much the same. Definitely see her being in the moses basket until she outgrows it, which is £34.00 well spent in my mind
Grobags - I bought a few of these and then DD turned out to be a 6lb 1oz tiddler, so was very glad I also got some blankets and sheets for back-up! We're actually swaddling her in the evenings now as it keeps her much more settled, so won't be changing onto the grobags for a little while yet. With grobags you don't have to put them feet-to-foot, unless you are putting blankets over them while they are in the bag.
Clothing - DD pretty much lives in vests with sleepsuits/onesies over the top. We bought a pack of 7 vests and about 5 sleepsuits and it would have been fine, except she was such a teeny little thing DH had to go out shopping the next day for "tiny baby" sizes. In my experience, people do give you clothes, but you'll get a wide range of sizes (my nan bought her a snow suit in 6-9 months size for example) but they tend to give you the more fancy things and outfits, rather than nice practical vests and sleepsuits. ASDA do nice packs of vests for £5 so it's worth getting some even if people do give you practical things.
Bouncer - DD at 7 weeks is only just starting to be interested in her bouncer, and it's certainly not the magical off switch that sends her to sleep that they market them as! It's a godsend now when she's wide awake and I need to plonk her somewhere for five minutes while I go to the loo/grab a sandwich/hide, but she really disliked it for the first few weeks. Even now, I put her in it with all its lovely lights and music on the activity bar (we got the Fisher Price rainforest one) and DD ignores the bar completely and gazes at the Christmas tree. Not tried a sling as I have bad hips/back but can see how it would be very handy.
Other things which have been useful...Our travel system which has a carrycot attachment has also been fab, she sleeps in that downstairs. We love the fisher price aquarium bath (as does she). We've got loads of muslins (and they're constantly in the wash cycle, very useful) but again, DD is a bit of a sicky baby so that might not be as essential for you. We get through bibs like no tomorrow as well. Cardigans, hats and booties are essential for going out for us, as we use a flat pram we can layer with blankets which are alot easier to deal with than snowsuits when you're in an out of places it's really easy for them to overheat if they're done up for the cold weather and its a pest to be constantly getting them in an out of clothes when you can just shift blankets around instead.
Good luck :D