The question you are asking is a lot more difficult to answer than just one caliber of firearm. Because of that I have a couple of different answers and some thoughts.
My initial response was a .44 mag/special. This would give you a .44 snub for self defense, a .44 pistol with longer barrel for home defense/hunting and a 44 mag lever action for hunting. It would make a good survival set up as well. Downside is that they are not common guns to pick up.
If you are are really talking a SHTF scenario where we are talking a breakdown of society to the point we are back in the late 1800s type atmosphere then I have different thoughts.
.22LR - great caliber and you can carry a lot of ammo on you for it. The mere presence of a firearm is usually enough to deter someone for self defense but NOT a self defense round I would count on if you had to use it. A rifle in this caliber can be used to not only take any game that walks here in Ohio but generally anywhere in the CONUS with a well placed (head) shot. Also, its such a common round that it should remain available through scavenging etc in a true TEOTWAKI scenario. If you are skilled with a .22 rifle you could easily keep someone's head down with accurate fire out to at least 100 yards if practiced for defensive purposes.
Shotgun - great option and needs to be a part of a survival scenario as it can not only be a very good close quarters defensive weapon but also allows for hunting via either shot or slugs. Downside is weight of the rounds in comparison to .22LR.
Rifle for longer distance hunting/defensive use - I would lean towards a military caliber such as 5.56 or 7.62 because of availability of ammo in a true breakdown of society situation. A 7mmmag is a great gun until you have to figure out how to feed it...and normally (except in these unusual times there is plenty of military caliber ammo on store shelves). Everything with this will be a give and take as 5.56 can be set up for great close up defensive use but lacks power as you get past 400 yards, whereas 7.62x51 rifles are not as easy to use in a close quarters situation but definitely can be used defensively past 600 yards or longer if you have the set up and the ability.
Pistols I would consider in a similar light. Stay with military calibers if possible. You also get into the semiauto vs wheelgun debate. Wheelguns are much more reliable as they have less parts but when they have an issue its a very catostrophic new pistol type of failure. Semiautos can breakdown in other areas and have more issues in general but a failure with them is usually not a catastrophic failure of the entire pistol. Magazines and pieces which wear out (slide springs, etc) will be the pieces to also stock up on.
With unlimited funds and unlimited ammo how I would want to be outfitted would also depend on how I planned on making it through TEOTWAKI scenario. Am I mobile and moving around? Am I staying in one location and defending it at all costs?