Hire a car for 3 days, you mean? Not a good idea. if you are looking for car to go to your hotel, it's easily available. If more than 2 ppl the hire entire cab. will cost 800 bahts and if alone or 2 ppl. Hire a shared limo. cost 150 baht per person.
In Pkuket you will go for mostly island tours. these tours are for 8-10 hours in boat. These tours cover hotel pickup and drop as well. So unless you only intend to see Phuket via road not a good idea. hope this helps. check out our recent Phuket itinerary for more info. it's on our Tripoto profi
I recommend you to install Grab , it's a online cab and food delivery service in South Asia(Indonesia,Cambodia,Malaysia,Singapore) and I bet their tarriff are much cheaper than the normal taxis , it's just like Uber and Ola
I would recommend you to not rely on Grab much as it can be costly sometimes. You will be able to get a shared vehicle from phuket airport in 150Bhat per person. Take the shared vehicle from then and then rent a bike from around your hotel/hostel. You'll be able to rent a bike in Phuket in around 250Bhat per day but one major problem with that is you will have to submit your original passport to the owner of the bike. Some might even give you the option to submit security amount in place of passport but that is generally very high. Some of the owners were even asking a security of 10K Bhat for one Bike. This goes the same for car as well. Petrol is cheap in Thailand so that wouldn't be a problem. A basic car might cost you around 1K to 1.2K per day.