Hi there,
It is a wonderful place. The word for rental in French is "Location" - so google locations vacances, sainte Anne, Martinique and you should get some good deals depending on the space and trimmings that you want. Some come with car rental. Otherwise shop around - there can be huge differences between rental companies. If you want to buy a place then buy a car too ! A studio in or near Sainte Anne will set you back 40 to 60.000 €. A small house 150.000 € and upwards depending on location and construction quality and features. Watch out for flood water zones or areas too exposed to the occasional hurricane.
Shopping is not cheap due to the 40 % import tax on just about everything. The Leader Price discount store offers good price/quality but you'll need a car to get to any major supermarket or commercial centre. There's a Dia discount store in le Marin which is very close to Sainte Anne - about 10 minutes away.
Petrol and diesel are quite expensive. But the island is small - only 40km x 15km. Sainte Anne's saving grace is its location in the south - far from the beaten track. But then again that also will boost your mileage. However. It's always great to get back to Sainte Anne !
There's fresh fish to buy everyday at the market - where you can buy drinks and juices too. Several small restaurants offer decent food at very reasonable prices. There are a few bars so you can keep topping up on those "ti-punch" ! A dash of lime, sugarcanne and rhum to keep you going.. !
I'd go for something near the village or "Bourg" as they call it - within walking distance. Otherwise there is a lot of choice around. Get familiar with the geography of the area and place names and ask for precise locations so you can check out distance to the village via Google maps, etc.
Lovely people around there - some English speakers too so don't worry too much - you'll be fine !
All the best,
Philip