Hi. Can't recommend a specific brand but would suggest a combination of stainless saucepans and non-stick frying and saute pans. However, be aware that some people will not use non-stick because of health concerns so have enough options. A variety of types and sizes are usually in any stainless set you find. One you might have to buy separately is a large covered pot for cooking pasta - guests will want one of those. And don't forget some basic baking pans like a muffin tin and cookie sheet. You never know how much guests will want to cook.
The only difference for gas or electric is if your electric stove has solid surface burners - in that case the pans you buy must have perfectly flat bottoms or they won't heat properly. We found that out the hard way!
I'm one of those people who worry about the chemicals in non-stick frying pans, so I don't keep any in my own house. When I initially furnished my rental, I stuck to quality stainless. But after a year or so, I gave in and added a few non-stick frying pans -- some people just don't know how to scramble eggs in anything but non-stick. Give them a choice, make everyone happy!
The size and type of pans you get will depend on the size of your house. If your house sleeps 10+, make sure you have lots of big pots and pans. If it's a cozy cabin for 2-4, then smaller pans are fine. In my big house, I added a roaster and a turkey baster when I started getting Thanksgiving and Christmas renters. I also have pie tins, cake pans, and a quiche pan in case someone is really inspired to cook!
I also stock a mix of sizes and types of pots and pans at my home.
My home sleeps 8-10 and my kitchen is large and used frequently by myself and our guests. Becuase I like to cook for my family when we visit, I have acquired a range of stainless steel pots and pans, from a small covered sauce pan for preparing sauces to an enormous pot for preparing lobsters or ears of corn (both foods are New England summer favorites and the lobster pot is a must at a coastal rental).
I supply three sizes of non-stick frying pans because, as other have noted, guests like to use non-sick pans. I replace them every year as the finish becomes scratched and pock-marked from use of inappropriate utensils (I supply the proper utensils, but I expect to have ruined pans at the end of each season).
I have a mix of mid to high level quality brands (Calphalon, Cuisinart, Farberware) because I usually turn over pots from my primary home's kitchen to my vacation home.
I recommend purchasing quality brands that can be placed in the dishwasher. Many of my primary home purchases are high end and hand washing is recommended. Vacation guests will not hand wash pots and pans. In my experience, even very large baking sheets and roaster pans are manipulated into the dishwasher racks. (The same is true of cutlery, but that's another topic . . . . )
When I have purchased for my vacation home I have found stores such as TJ Maxx, Homegoods, Marshall's, and Costco, to have a good selection of quality pots at reasonable prices. A matched set is not required.
Be certain to supply a vegetable steamer - very popular with health conscious guests.
When I started renting, nearly twenty years ago, I purchased lesser quality pots and pans - I learned my lesson as not only do they not perform very well, they deteriorate rapidly. Also, it's impossible to advertise a fully equipped kitchen if it's stocked with poor quality equipment.
If you have solicited feedback from your guests you will have a good idea of what works and does not work in the kitchen; my guests have requested certain types of pots and pans over the years, and if a request is reasonable, I am happy to provide it the following season.
I buy fairly good non stick pans, a 3 pack from Costco, that I have to replace about every 2 years. I would never buy non stick sauce pans. Costco has a Kirkland tri-ply set of stainless that is as close to All-Clad as I've seen, and the whole set is around $200. If you're at the beach, be sure to get one of those cheap big clam steamers for crabs. My renters REALLY like the 2 sizes of electric skillets I got. They're not cheap (CucinaPro all stainless), but they're almost indestructible, even will go in dishwasher. NEVER get a non stick electric skillet, total waste of money because it won't last. I also have a big stock pot with pasta insert (I don't think that's necessary) and a steamer basket that will hold at least 2 lb of shrimp (really necessary at the beach). That's a big Cuisinart. We use our cottage and kitchen frequently in the off season, and that's my excuse for getting the good stuff. I also got some old iron skillets that I reseasoned, very inexpensive. I'm fairly certain that you will come out ahead in the long run monetarily by purchasing good quality equipment, not to mention the stress of finding destroyed pots and pans and having to spend your time getting new ones.
Good luck and have fun shopping,