You're best bet is to head over to tripadvisor, go to Majorca and click on the forum posts. There will be loads of good info there about good national and local companies to use. Just from personal experience don't touch Goldcar.
I go to Menorca all the time and always book through holidayautos. Lots of choice with info to help you pick what you want.
I have used several companies from the airport at Palma. By far the best, cheapest and quickest is Hertz. Their desk is on the right as you leave the airport. You can book on line direct on their website.
If I was you, I would just get some info from the concierge in your hotel. I have hired cars all over the world. As long as you check out the cars that are offered for the price, there isn`t usually a problem. I have driven a hire car in Majorca but I can`t remember which company we used. It wasn`t a global brand but it was perfectly OK.
Yes locals will usually recommend good local companies but they are often a lot more expensive than the multinationals. It depends what your priorities are. I'm guessing that you may want pick-up from the airport though so all organised before you arrive.
Don't go for the cheapest.Try and get a company that give full/full or same fuel option. Unless you plan to use all fuel, full bring back empty company Stay clear of GoldCar
If you shop at Tesco and get their rewards vouchers, you can use them for car hire with Affordable Car Hire who are like an agency, but use all the well known firms (Budget, Avis etc). We hired a car through them in the US and paid for it all with vouchers except for about £20 insurance. Have a look on the travel section of Tesco's website.