When I go over bumps/potholes in my Civic, it's enough to rattle my teeth out.

It drives ok, but I can feel every single bump in the road and it sounds terrible. Car has 222k miles and I've never done anything to the stock suspension.

While I've done a lot of maintenance to my car myself (the usual oil, ATF, brake pad changes, plus timing belt and radiator changes), I have to admit I'm completely ignorant when it comes to suspension.

I'm guessing some parts of my suspension are shot. If you were me, what would you do to fix the car? What would you inspect? I'm thinking of taking the car to a trusted mechanic since I don't have the time or possible tools to fix it. What should I ask him to do for me?

with that mileage, if its original suspension then what you are experiencing would be normal,

if it really bothers you then an entire new set of shocks/struts all around would be what you want

also get all your bushings inspected, the most common ones to go are the front lower control arm bushings,

also, the front end sway bar bushings can cause a lot of clunking over bumps,

its best to take it to a shop that specializes in front end and suspension work

Don't forget the ball joints, tie rod ends, and sway bar links.

At a quarter million miles it could be anything and everything, maybe stuff most people would never get to see.

A Basic suspension inspection should be done

FYI sometimes it's damn tough to point at Hondas struts and say it's a problem when it is not leaking or obvious.
(They sometimes knock without any outward clues it's inside the strut)
Sometimes it has to be a guess or a process of elimination.

How much should I budget for all this?

I know it's impossible to say, but any ballpark guesses?

Budget enough for an inspection and estimate? Then decide what to do after that.

I'm in the process of redoing a 236,000 mile 02 Civic EX.
The bill from Rockauto is $430 including shipping.
That's for 4 struts (budget ones)
Good quality ball joints & outer tie rod ends.
Some other little stuff, exhaust doughnut, transmission axle shaft seals, oil filter, front lower control arm bushings and so forth.

I checked the sway bar links & bushings and they were OK.

I had put everything for suspension & steering into my shopping cart at Rockauto. Then when something checked out as OK, I removed that part from the cart. When everything for suspension was in there, including axles, all the sway bar links the total was $750. (no wheel bearings though)

that's why I like these 7th generation Civics. Parts are relatively affordable.