I found the best prices muslins at Matalan...they do plain and cute designs. Seem as good quality as elsewhere twice the price and do the same job!! I got lots of cellular blankets from mothercare and although they were slightly more expensive that some shops they seems to do well in the wash and feel a bit nicer!
Ikea sell little wash cloths called KRAMA for a few pounds and they have been invaluable... from newborn through to toddler. They are thin soft little flannels and after buying lots of expensive muslins I found these did the job far better at mopping up spit up and barely used the muslins. Not sure on blankets as most of ours were gifts!
We bought loads of muslins from Primark, some from Asda as well. My DD is 3.5 and they're her comforters, she has loads (currently in bed with about 10 of them) and I've bought her a pack of rainbow ones from Tesco for Christmas. They can be a bit rough, so we bought some lovely soft scarves from Primark and my clever DM turned them into muslins of a fashion. I wouldn't use them for wiping up spills but they're good to snuggle with.
Apart from the time DS was born til he went into a sleeping bag at 8 weeks I didn’t use more than 2 cellular blankets. So you don’t need to buy too many. DS also hardly ever vommed, now he’s starting to wean they’re coming in useful, use them knitted behind his head as a big bib. Only ever used them as something for him to play with so far 🙈
I bought loads of cellular blankets and probably used two of them a couple of times. Dd went into a grobag as soon as she got to 8lbs and they were no good as pram blankets. I would just get a couple to start with. Ours were lollipop lane from amazon and were lovely and soft. The best muslins were actually hand-me-down ones. They seem to get softer with age. I cut some into small squares. They are great for drying little bums and Dd has never had nappy rash.
Agree with Roses. No need to stock up on cellular blankets, I bought several from JL and ended up giving them away several years later, unused. DC just had a fleece over them in the Moses basket and then we used sleeping bags.
Muslins... I just worked my way through Mothercare ones and they were fine and washed well.
With online shopping/Amazon you can have stuff delivered the next day in a real emergency. With hindsight I wouldn't have bought much bedding beforehand but the marketing guys convince you that you need to have it all ready!