I don't know if my situation is valuable to you, but I just took over managing my parents' duplex. It started as a long term rental, but we live in a beach town, so they decided to do vacation rentals for 3-4 months and look for long-term rentals in the off-season. There is a long-term rental shortage in our area, so I'm not worried about placing people in the off season. Fortunately, I have very good documentation from them on their prices, vacancy rates, and expenses, so I could get a pretty good estimate on what I would make through management.
If you're not sure about those numbers, take a look at other vacation rentals in your area using Homeaway / VRBO or AirBNB. It's similar to finding comps for purchasing a property. See what other similar properties are renting for. Another solution is to contact a local property management company and ask what they charge, and see if they'll give you a vacancy rate as well.
You can charge significantly more for a short term rental, but you end up doing a lot more work as well. Also, utilities will be covered by you, which may or may not have been the case when doing long-term rentals. It will need to be furnished as well. Your vacancy rate will be a little tougher to predict until you have a couple seasons/years under your belt.
Generally, people determine a nightly rate for their property, then commonly offer a discounted weekly rate, and sometimes a further discounted monthly rate. Depending on the demand in your area, it can be advantages to require a minimum length of stay (3 nights, 6 nights, etc.). The longer the stay, the fewer times you need to clean the property, or have it cleaned. It's generally a good idea to charge a non-refundable cleaning fee on top of your rental fee.
Make sure you build systems to catch yourself. You'll potentially be juggling a number of different potential renters and it can be easy to let someone slip through the cracks. Even worse, you run the risk of double-booking, which isn't something you generally need to consider when doing a long-term rental.
Let me know if you have any other questions. I'm just getting into it myself, but I've been learning a lot from BP as well as from my parents, who have been doing this for a number of years.
Brett Fitzgerald