"For loading 7MM-08, 204 and 223 ammo, could the Lee press and powder measure work Ok."
Certainly. Since Lee makes several presses that differ widely, not sure what "the Lee press" you are looking at but they couldn't have survived so long in the market if they didn't work quite well. I really like some of Lee's tools but no brand is my "favorite". All makers offer some tools that meet my needs very well so I don't promote or slime any brand, it all depends on how well each item actually works but I can use anything to succesfully make good ammo.
I have an RCBS Rock Chucker II for my main rifle press, a Lyman turret for handguns and two of Lee's very small "Reloader" "C" presses dedicated to de- and re-priming. That's just saying what I have, not what I would recommend to anyone.
A few years back I got a new dial indicator and magnetic base for it. While playing around I checked the press spring of my RC when FL sizing a few .30-06 cases. Got about .003" average deflection and that's really not much. Then, just for kicks, I repeated it on each of the Lee's. To my surprise, the indicator needle didn't move enough to get a figure but it was well under .001"! Meaning, even the smallest Lee "C" press deflected MUCH less than my much lauded RC II! (Didn't bother to check the Lyman turret, I KNOW it springs a lot.)
If I had to replace my main press tomorrow, it would be a Lee Classic Cast single stage. It's inexpensive, bigger than my RC II, VERY strong (cast steel, not iron), the primer catcher actually seems to work properly and the lever is fully adjustable. And it's ALL made in the USA, not China. That's the press I would recommend to anyone, at any price!
My powder measure is a Redding Master, forerunner of the present 3BR. It's as good as it gets for measures of its type but still not great with coarse powders. Lee's little plastic body "Perfect" powder measure has a reputation for "leaking" ball powders unless it's properly assembled and adjusted, but it also has the embarassing reputation of beng perhaps the most consistant measure to dispense the more coarse powders many of us prefer for rifles.
Lee's little "Safety" powder scale works, it's sensitive and accurate. But, it's really jerky-querky! Ain't no way I'd put up with tryng to use it long. Get Redding or RCBS 505 scale instead.
Anyone's dies will work well fine.
The various "quik-change" die bushing systems are a solution to a problem I don't have. Just don't see how screwing a die in and out, hand tight as they should be, is too time consuming. And with several set of dies, the cost of a bushing for each die can get expensive prettty quick. But they do work, up to the owner to make that decision for himself.