Even with the windshield, running an open and a hybrid helmet (open face with a chin bar), and with sunglasses, I always used to get grit in my eyes. Hasn't been an issue once since I switched to full face. It's a little warmer, but I feel so much more comfortable behind the wheel.
Check with your track day org and see if you can run an M rated helmet, or if it has to be SA. Motorcycle helmets can often be had a little cheaper, but have slightly different requirements.
As far as a make & model recommendation, the best recommendation I can give is go somewhere that sells them (motorcycle store, if you can use M helmets) or a safety supply house and try a bunch on. There are a bunch of different head shapes and shells to accommodate said shapes, and it's hard to know what will exactly fit your melon without trying them on.
Also, when you're baking in the sun: Lighter colors are better than darker colors.