Unless they've changed the rules...I wouldn't recommend going to Katara beach! No bikinis....so you'd have to wear a t-shirt and shorts.
Intercon is always a safe option, with a nice beach...Sharq is nice, but quite a lot of planes overhead!
Sealine Resort is a nice 'cheap' option outside of Doha...not brilliant quality, but ticks the boxes!
Otherwise, head to the Inland Sea, or over to Dukan if you want to explore. Enjoy!