If you're not planning to finish it with a coat of exterior grade poly, wipe it down with mineral oil, especially the top. Pour on the oil and spread it around. Keep applying until it won't absorb any more. (I'd either paint or poly the apron and legs.)
Mineral oil is food grade and is often used for wooden cutting boards and cooking utensils. Helps protect the wood from water damage and stains. Also helps stop the absorption of grease (raw or rendered) from foods.
FWIW, I used mineral oil for the finish on a new shelf for my CG.
Handles: An easy handle is a screen door handle. Check out the door hardware section at Lowes. If memory serves, they have several sizes. A more "fancy" handle that can also serve as a towel bar can be made from two wooden shelf brackets with a section of closet rod mounted between them. (Think oversize paper towel holder mounted to the end.)
If you have the space, trick it out further with a bar sink installed on the other end. You can gain the counter space back by placing a small cutting board over the sink, when it isn't in use. Let me know if you're interested and I'll give you the info on the hardware needed to make the hookup to a garden hose.
To keep the weight down, if you decide to add a shelf, is to look into the wire shelving used for closet organizers. Or, consider using hardware cloth stapled to 1x3 shelf supports.
Again, great job on a custom home for your pit. I love to see backyard DIY projects. Thanks for sharing.
CharGriller Super Pro SFB
Sunbeam gas grill