PDorsey,
A 5/8 round point is ideal for starters. You'll do well with a 6/8 round point, too, but a 5/8 is a sure bet. Whether new production or vintage, please make sure it is shave ready. I suggest staying away from eBay until you know your way around the straight razor world — because eBay is stuffed with lofty descriptions of razor that are not up to par when viewed in hand. Also, when you read "shave ready" on eBay, most likely the razor is not. Anyway, buy from the Classified here or a reputable vendor. Finally, don't buy your razor sight unseen. Know what you're buying.