Tex is a better evangelist than I ever was, but I've been saying the same things about combo for years. My teams used to all be zone/press combo. And I've only ever spent 10 minutes on the press. Zone is the base defense, press is just there for some additional TOV/g. You don't need 8 guys at B+ or better for it to work.
I have a D3 title and a couple D2 titles with the combo, but notably I don't play them anymore. A) I'm kind of bored with it, but also B) it doesn't work as well since D1 has become more populated. One of the side effects of higher population up there is that those teams are coming down for the 75-150 ranked by position players more often, and those are the backbone of high level D2 teams. That's fine, affects everyone, except with the extra ~10 minutes you're using for the press, reaching down for lower starting players with upside is more costly. You need guys who can get to elite level on their own, quickly, and it's a tightrope when C- teams keep dropping in heavy on recruits 3 cycles before the end of the 1st session. It puts a premium on location and knowing who is in your area, and what they need, and that's all just too much work for me these days.
To OP, speed is important for the press. In a straight press, you are trying to win by creating turnovers and winning the TOV battle. That is driven by the speed of your guards. I have speed as a little more important than defense for guards, and about even for SF. I don't give speed much thought for the front court, unless I'm thinking about whether they can handle a high distribution or not, and that's got nothing to do with pressing. Athleticism is important too even for guards, for avoiding fouls; and obviously stamina is right there with it, unless you run 12 deep comfortably, and don't mind slowing down.