1st time in Riyadh

Welcome aboard; and soon to Riyadh as well.

Let your company (or their agency) find an apartment for you.

Other options may be:

1- Look for advertisements online:
Check out: https://www.expat.com/en/housing/middle … ia/riyadh/
and http://www.expatriates.com/classifieds/ … available/

Expect people moving out with residual rents. Some selling their belongings along as well. Please note that rents here are usually paid upfront 6 or 12 months.

2- The traditional way - In my experience the best deals come via this way.
Walk or drive around in the area you are targeting to live in. You'll find sign-boards in Arabic saying "For rent". Just call the number written and start inquiring.  You need to know Arabic if you wanna go this way.

Initially use taxis to move around. To buy a car, you'll need to get the drv license first.

Furniture: Ikea or Home Center showrooms.

zaahib.com and bey3.com are also good sites for apartments. Are you single or married? That will effect the quality and number of apartments you can rent.

Thanks for your prompted response.
Quick question, if I want to travel to Bahrain or UAE for a weekend, do I need to get exit/re-entry?

Yes, please make sure you have it in writing. It is best to get the multiple entry visa.