Just my 2-cents

All will do the job, dead is dead! Based on ballistics and my personal favorites, they are listed below in order of preference. But if I had to choose one cartridge from my list as a do all then the 243 Winchester would get my vote. Even though I have a soft heart when it comes to my Swift, the reality is it has limited uses and is kind of a safe queen because of this. When shooting prairie dogs in Western Kansas it is the first thing I grab. It makes it rain chunks with red rainbows. With a 243 you can shoot lighter bullets for thin skinned varmints or loaded with heavier bullets to harvest animal as large as Mule deer. So if you are looking for a multi-purpose cartridge go with a 243. If you are looking to add to your collection then the 22-250 Remington would be my choice as an addition.

220 Swift
1st choice - 55 grain Nosler Ballistic Tips at just over 3,800 fps
2nd choice is 36 grain Barnes Varmint Grenade at just over 4,300 fps

22-250 Remington is more prevalent than the Swift, ammo is easier to locate, and the difference of 200 fps (slower than the swift) whatever you shoot won't know the difference.
243 Winchester is even easier to locate ammo for than either of the other two. It is more versatile than any of the smaller cartridges. In my opinion it is the transitional cartridge between varmints and medium to large game. On more than one occasion I have witnessed a 243 Winchester drop a Mule Deer at distances of 350-400 yards, none of which have taken another step.

Overall I have most likely killed more coyotes with a 270 than any other round. I only owned two centerfire rifles in my younger days (until I was 35 or so) a 270 and a 30-06. I shot the 270 out on jackrabbits and coyotes. Very effective.

If I wanted to build a 243 specifically for about 55 grain varmint rounds, what twist would be best?

Just a quick calculation:
Nosler 24055 (.243) Ballistic Tip 55 grain (bullet length = .787")
2900 fps
Bullet Gyroscopic Stability (GS): Jacketed = 10
Twist Rate = 13.5:1

There are several factors, but this is a quick (in the ball park) calculation.

I would stay around 10 twist. My 22-250 is a 1-12 shooting 53 grain bullets, it likes very few bullets above 55 grain. The standard for a 223 is 1-7 to 1-9.

2900fps for a 55g 243 is extremely slow, should be in the 3400-3600 range pretty easily.

haven't we beat this dead horse to death

Biden?

Unfortunately that horse isn't dead yet.

Don't care about pelts and generally will be shooting and calling. Currently I am using a 243 pushing Nosler 55 gr. Ballistic Tips around 3800 fps. Thinking about putting together a 22-250AI with a 1-12 twist and shooting 40 to 55 grain Ballistic Tips. I guess I could build a 224 creed with a 1-12 twist. Brass isn't hard to come by either way.

I wouldn’t do an AI just due to fire forming and it’s really not gaining you much over the 243