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I had the same concerns as well when I got mine removed.

So let's be real about things. The procedure itself was the most uncomfortable one because it took a long time. There was no pain, just discomfort of someone working inside my mouth. I was given pain meds and easy-to-follow instructions. I had scrambled eggs and yogurt for a good week or two, which got boring because I didn't prepare well. I followed my pain med instructions easily.

2 years after, and I have no issues. So, as long as you're not an idiot and as long as you don't deliberately fail to follow instructions, it'll be alright. Do it, don't put it off for longer.

Statistically you're unlikely to have lasting issues as a result of getting them removed. It's a very common outpatient procedure.

When you go in, they'll likely give you nitrous oxide, which will make you relax a little, and they'll let you sit and breathe it for a few minutes. I'd recommend bringing headphones since some nice music will help.
Then they'll give you an IV that will make you not worry and likely barely remember what comes next. Basically a big dose of super valium.
Then they'll give you some pain killers and local anesthetic and remove the teeth.

Your memory and orientation will start to come back in about an hour, by which time hopefully the person who transported you has gotten you home. You will not be able to care for yourself during the intervening time. You will be uncoordinated and of poor judgement.

When you get home it's best to try to sleep until the meds that the dentist gave you wear off, or just watch TV. Take ibuprofen or Tylenol mostly, but an occasional opioid will help since there is some pain that the antiinflammatories don't help with as much, although they take care of most of it.
Soft foods for a few days, and no straws.

All in all, you should be back to normal within two weeks, and you'll get to feel nice and excited to eat something crunchy or chewy.

If you've had pain associated with your wisdom teeth, I'd recommend going forward as scheduled. The pain may have gone away temporarily, but it'll come back.
I let mine go too long, and one of the wisdom teeth cracked open because of pressure on it from another tooth, which also damaged that tooth which was fortunately able to be repaired.
The pain from waiting for outstripped the discomfort of the procedure.

I recommend you don't wait. I didn't have mine removed until after they were impacted and my teeth began to shift. They were cut up before they could be removed. My only lasting side effect was from waiting too long. 20 years later I'm using Invisalign to straighten my teeth.

I got all four removed at the same time, my dentist put me on anti-inflammatory medication for a couple of days before the procedure and gave me a steroid to take the morning before the procedure.

I was maybe 20 years old or something like that, roots were so messed up he asked if he could keep the teeth and show his colleagues how messed up they are.

It doesn't take long, there is no pain but it feels really uncomfortable, normally he would have just given me more anti-inflammatory medication but after seeing the roots, he gave me a small supply of Vicodin to get through the first few days.

Afterwards, my mouth was pretty sore and I pretty much only had broth for a week.

Popsicles are great, keeping your mouth cold will help with inflammation, and you might want to try to sleep on your back, rolling over and hitting a cheek won't be fun.

Mooncabbage is giving some excellent advice already but one more tip: I had the option to spend 10 bucks to (directly after surgery) have a mesh of fine tubes on my face for 30 minutes through which they pumped really cold water. I was still drowsy and barely remember it BUT I had very little swelling and I think the cold mesh immediately after the procedure did it.

I had a wisdom tooth removed when I was younger. They anaesthetized me, so I don't remember the actual surgery. Since you're removing three at a time, there will be a lot of swelling as you've probably been told. I would suggest you get some Soylent if possible, though that can get boring really quick. As others have said, scrambled eggs, yoghurt, soup, mashed potatoes, etc. I suppose you could also have regular meals and shove them in blender and eat that way.

I wouldn't sweat it with the surgery itself, it's such an old, well practised surgery there is very little that can go wrong.