You'll need to spend a little time thinking about what you find important in an appliance, and it would also be helpful for you to know the size of the openings in your house for those appliances (unless you haven't finished the kitchen/laundry rooms yet and are waiting on appliances). Do you want a fridge with a top freezer, bottom freezer, or size freezer? Do you want black, stainless, white, or some other color? Do you need a gas or electric stove? Do you want a large or small washer and dryer?
Put a short list together of what you would prefer - window shop at appliance stores or HD/Lowe's to see how you like some features.
When you're ready to buy, your first place to look should be Marketplace, Craigslist, etc. Plenty of people post perfectly usable if not downright pristine appliances for sale because of a wide number of reasons. If you have time to look, I bet over the course of a few weeks you can pick up at least half of what you need for a tiny fraction of list price.
Next place to look should be scratch-and-dent stores. Sometimes the big box stores will have "Damaged" or floor model appliances out on discount, but you'll have better luck at stores which are dedicated to selling these. Most of the time, they're completely perfect except for some cosmetic damage (or at worst, a broken button or latch), again for a pretty big discount off list.
If you MUST buy new from a big box store, try and wait until they're running appliance sales (happens a few times a year). Definitely don't get sold on fancy tech or lights or colors - just look for what you need. The only other good reason to buy from a bigger store is the warranty you might be able to get. Costco will give you a pretty beefy warranty, even if they have a very limited selection.
A few more general points:
Avoid Samsung and LG appliances at all costs - they are notorious for failing right after the warranty period is over. Don't tempt yourself into buying one of these dirt cheap either, unless you're able to replace a compressor or main board yourself.
Try and steer clear of anything that relies too heavily on digital/non tactile controls. It's just another point of failure.
Go for a top-loading washer if you can. They may be less water efficient but they're also less likely to fail and there's fewer gaskets that need to be kept clean.
Don't just shop by rating, look at reviews across different platforms and see what people are saying about them when things go wrong. If a washer isn't cleaning clothes as well as someone would expect, that's a world of difference vs. 15 people whose control boards shorted out and they can't get them repaired out of warranty.
