Here is a list of what I carry. This is not what I suggest you should carry, far from it. I only put it here as a note of interest, if you choose to use it as a guide that is fair enough, it has worked for me and continues to do so.
I suggest that you look to yourself as to what you are comfortable to carry and can wield with a reasonable degree of skill.
Primary weapons:
I carry at most times a Remington 700 bolt action rifle in .308 it has a scope and happily eats through any .308 round I care to put through it. I don't carry it at all times due to its weight, and sometimes I want to travel lighter.
At other times I carry a Marlin model 60 semi automatic in .22lr. This also has a scope, and holds eighteen rounds in a tube under the barrel.
I try to avoid carrying a firearm and only take one if I feel am really going to need it. I know, I can hear you all gasping, and this plan has got me into trouble a couple of times, but if I carry a gun the temptation is to use it. It can give unfounded confidence and cause you to take risks which you might otherwise avoid. I know myself well enough to know that if I leave the guns when I venture out on the most part it will give me a better chance of returning to them.
My most common primary is a large two handed felling axe, this is my bread and butter and has saved my life more often then I want to remember. There is nothing special about it but I keep it razor sharp, and practice with it most days. I have named it Snaga from a book I read once, although it lacks that axes beauty, it does not want for effectiveness.
Secondary weapons:
As my first back ups I carry two hand axes, again I keep them very sharp, blunt blades still work, but the sharper the better!
Next is my Gerber MkII fighting knife. It is a bit desperate if I have had to pull this, but I have had to in the past and probably will have to pull it again in the future although I hope to avoid that.
I also carry a Winchester riot boot knife, I thank whichever deity is out there that I have not yet had to draw this in anger. I hate to think how dire the situation would have to be for me to use this.
Lastly I have a reasonable lock knife, this is used for mainly general knife duties, but at a push the blade is long enough and sharp enough to kill a zombie. I don't ever, ever, ever want to have to prove that.