Hi, and welcome. Short term is definitely the best way to go so you have some breathing space to find something permanent.
You pay a premium for short term accommodation, but it's far better value than a hotel. Depending on your budget and where you'd prefer to stay you have the following option;

Real Estate Agents specializing in Short Term;
Mirage Real Estate - They have 3 buildings that offer monthly rentals.
Homes 2 Rent - Have a number of building offer monthly rent.

Operators ;
Holiday Villa - Al Muntezah, Central, good quality with 2 & 3 bed units.
Ezdan Suites - West Bay. Bad rep, but good for short term. Good facilities. As long as short term, it's fine.

These will get you started! My company can help you with long term accommodation when you arrive. Feel free to PM me if you want any info on prices etc.

Good luck!