The problem with most of the boats you're going to find is that something in the 34-36' range is going to be a bit tight for four or five people aboard for a week, but anything that would be comfortable for five people for a week is probably going to be much bigger and more expensive than you would want. As my friend says about his C&C 38... Sails 6, feeds 4, sleeps 2.

And for anything over an extended weekend, he's right.
The best boat buying advice I was given is that the
"Primary use of a boat is Primary." If you want a boat that you can single-hand and liveaboard... and that is your primary use....get one that you will be comfortable single handing, that is large enough to live aboard.... and if it is tight with five people aboard for a week... learn to live with it.
I'd also recommend that you reserve about 15-20% of your actual boat buying budget for refitting, repairing, modifying and upgrading whatever boat you end up getting. Boats are not like cars—they're not ready to go out of the box most of the time. Generally, you'll find that you may want to change the way the running rigging is setup, or the way the genoa fairleads work—like going from a pin stop to a line-controlled genoa fairlead—to get the boat to work the way you want it to.
Given the type of sailing and other requirements you have, there are a lot of boats out there that could do what you need. Catalinas, Beneteaus, Jeanneaus, Tartan 34C, Hunter 37 Cherubini, various C&Cs, Endeavors, Ericsons, O'Days, and Pearsons... would all work for you. What you probably need to do is sail on a few boats and narrow the field down as to what else you're looking for in a boat.
For instance, do you want three cabins?? This would afford your guests when on the week-long sails a bit more privacy, although the individual cabins would be a bit smaller in size. Do you want a boat with a separate shower?? This is rather uncommon on boats smaller than 40' from what I've seen. Do you want two heads?
A few things I'd recommend, since you're planning on living aboard part-time. Look for a boat with a 12 VDC refrigeration system. Engine run refrigeration is a pain for a liveaboard. Get a boat with a decent electrical system that includes a decent size house bank as well as a good inverter charger. Check to see if you'll fit in the berths as well as for standing room in the cabin.
Since you'll be taking week-long cruises... check for a good ground tackle system... you'll need it unless you're planning on marina hopping. Even then, a good ground tackle system is cheap insurance...

You never know when you'll be caught out by bad weather, and having a good anchor to hold you in place is always a good thing.
Personally, since this is primarily for you to single-hand and liveaboard, I'd recommend you look for something in the 32-34' range, rather than anything larger... the larger the boat you get, the more expensive it will be to own, since the mooring/dock fees, haulout fees, and many of your maintenance costs go up with the length of the boat. Also, the equipment gets more expensive as you go up in size. Another reason to go and focus on the smaller boats, is that you're likely to be able to afford a newer one or one that is in better shape or better equipped, than you would if you went with a larger boat—in the short run this can save you a fair bit of money in terms of needed repairs and upgrades.