Here's what I know about clear coatings on wood after fooling around with boats for many years.
Any clear coat is more difficult to apply and maintain than paint and, as you might imagine, the prep work ahead of time is more tedious too. Varnish, in all it's variations, is subject rapid deterioration from sunlight and by the fact that varnish isn't waterproof. Moisture traveling through the layer of varnish, in and out of the wood substrate, causes deterioration. Buying better varnish with more UV protection will help as will applying more coats. Of course that means more money and time.
One viable option, and one I try to use on all my marine brightwork ("brightwork on a yacht means varnished wood, not polished brass") is to first coat the wood with a high quality clear epoxy which IS waterproof. That provides an ideal base for varnish and will make the finish last at least five times as long. The problem is that clear epoxy which will flow out as a nice coating, as opposed to the kind of epoxy you might use as an adhesive, is expensive and it's a bit of a PITA to apply and has it's own clean up procedure.
Epoxy is generally not very UV resistant, so you must over-coat it with a vanish-like product with good UV protection. If you let that surface go to Hell, the underlying epoxy will eventually turn cloudy and stripping epoxy is really labor intensive. Don't kid yourself. An epoxy clear coat covered by 5 or 6 coats of varnish will demand a huge amount of sanding, but the resulting finish will be long lasting and spectacular looking, although some yachtsmen will argue that it looks "too plastic".
If you're interested in a beautiful finish, over epoxy or over bare wood, sand and re-coat that finish BEFORE it shows any sign of deterioration other than a slight dulling of the finish. Of course, the best thing you can do to make your clear finish last is to keep it covered up and that's much easier to do with a grill than a boat.
So if you love fiddling around with things like a nicely finished wooden grill handle/table AND you're willing to spend the (considerable) time and money to maintain it, then go with something like West 207 Special Clear Hardener and 105 Epoxy Resin covered with Epifanes clear marine spar varnish. You'll invest quite a bit of money and a LOT of time, but the results will be jewel like and, if you cover your grill, the clear handle/table parts will last a long time.
But if it were me, I'd just sand the wooden parts and slap on a few coats of ordinary varnish, show off my handiwork to my buddies, keep the grill covered, and put off refinishing until the parts started pealing and looking really crappy. Then I'd strip the varnish-only finish using a chemical stripper, sand a little bit, and re-coat with cheap varnish. The wow factor with this method will be low, but so will the cost and the effort and the parts will look OK for at least a while right after you apply the finish.