I do not now, nor I have I ever owned a pressure cooker, and I cook practically every day. Not necessary at all to me, but how often do you think you would use it?
I do own a crock pot, but mine can also be used as a deep fryer and has adjustable temperature settings on it, so it does a bit more than your average crockpot. I don’t use mine a whole lot, but it does come in handy on a hot summer day when you don’t want to heat up the house with the oven, for instance. If you prefer to ‘set and forget,’ you could find a crock pot a useful item.
Out of the three things you mentioned, I do think the stand mixer is going to be the most useful - most people have already mentioned baking, but KitchenAid stand mixers do A LOT more than just mixing. You can get all kinds of attachments for them - shredders, slicers, juicers, grain mills, meat grinders, sausage makers, pasta rollers/cutters, ice cream makers - they are multi-purpose tools. My stand mixer is actually an old Kenwood model which came with a blender attachment and a catalog full of a whole slew of other stuff.
In the end a stand mixer may actually end up saving you a bit of space if you buy an attachment for it instead of purchasing a separate standalone item. They are heavy, but that’s a good thing. You don’t want to be mixing up a large amount of heavy dough and have the thing rock itself off the counter.
One thing about the planetary gear type mixers, though - they don’t do a great job at whipping egg whites, so you might want to keep your hand mixer around. That’s what I use for egg whites - it does a better job in about a quarter of the time.
I’ve heard stories about the things you can do with a pressure cooker - cooked whole chicken in half an hour, cooked-from-dry beans in an hour or so… but have never really felt the need for one.
I do have, and use, a Crock Pot, but sporadically. I’ll go a couple of months between uses sometimes. When I do get it set up and use it, it’s great.
Ditto stand mixer. If you’re doing any real baking it’s worth it. I have a handheld which gets used for any small tasks, but anything like cookie dough needs the stand mixer (my handheld is, admittedly, wimpy, but it struggled last week just making a batch of Nestle’s Toll House cookies). If you don’t do a lot of baking, a better-quality handheld might work for you. The uses romansperson mentions for the Kitchenaid mixer are real uses, but not things the average cook does, so I wouldn’t necessarily consider those when making the decision.