When I first had dd my aunty came round with a tub of snacks, large water bottle and a dvd box set.
She told me my priority was eating well, sleeping whenever I had the opportunity day or night, and establishing breastfeeding (if I wanted to, which I did).
She came into the house most days (mum not alive anymore so took her role) and wiped down the surfaces and threw the Hoover around. I got easy nutritious meals from her and other friends and everyone looked past the mess (or loaded the dishwasher if they did notice).
It got easier at 4 weeks when dd was sleeping a bit more reliably and feeding less frequently, and easier again at 3 months when she started sleeping for longer stretches and napping in the cot.
If the housework is getting you down, do get DH to help with the areas stressing you out, or pay for a cleaner, you'll both be tired but it doesn't take too much effort to do the basics. It's tough when you can see it, feel responsible for it, but don't have the opportunity to do anything about it.
Sleep deprivation is a killer, and it's the build up over time as well as day to day, so don't push yourself or you'll really struggle in a month or two.