The 38 Special cartridge was designed for black powder, being developed from the 38 Short Colt and 38 Long Colt cases that go back to 1875. As such, a 38 Special case is way "oversize" for the higher-energy smokeless powder that we all use today. (Black powder cartridges were pretty much fill-'er-up-and-stuff-a-bullet-on-top proposition: it simply was NOT POSSIBLE to put too much black powder in a black powder case.) So you will normally have quite a lot of extra space in a properly charged 38 Special case with MOST of the smokeless powders you're likely to use.
A 38 Special-power load that has its case full of
smokeless powder is approximately a 9mm Luger - put those two rounds side by side to see the power difference between black and smokeless powders. (There are a few smokeless powders that are just about as bulky as black powder, but the ones I tried years ago didn't meter very consistently in the powder measures that I used. Of course if you want to draw some attention at your range, can put up with impenetrable smoke with each shot and don't mind completely stripping a perfectly filthy gun to clean it with soap and hot water afterwards, just pack those cases full of black powder and blast away.
Do NOT, however, use a regular powder measure to meter black powder.)
Since the 357 Magnum is just a "stretched" 38 Special case (to be sure it couldn't be stuffed into older, weaker 38 Special guns) you might find even MORE empty space in a 357 case, although if you load for full magnum power you may end up with some of the slower burning powders that are themselves somewhat more bulky than fast burners like the perennial 38 Special favorite, Bullseye.
I have been using Lee equipment for decades to load many tens of thousands of rounds in a variety of calibers (including 38/357) and have found them to be a great value for the money. They DO take some fiddling from time to time, but I have yet to wear out any metal part on a Lee press. (Their "cheap plastic parts" are just that - cheap enough that you ought to keep spares on hand of any of the parts that wear. You can do that for a couple of lifetimes and never spend as much as you would for a Dillon, for example.)
RustyFN's advice for setting correct bullet seating depth is correct, BUT you must be aware that it will be "perfect" only if the bullet on your master cartridge is exactly the same shape as the bullets you're reloading with. If the shapes are not identical, you won't get an exact setting on the first try, and even if they are identical the pressure of seating a bullet is different than the pressure of just lowering the seating stem onto one, so you may have to tweak the setting in any event. Personally, I don't even try to get a precise fit the first time - I'll put a factory cartridge in the seating die (with the seating stem backed WAY out) and turn the stem down until it just contacts the bullet, THEN back it off a quarter or a half turn or so. Put a sized, flared empty case (you DO use an EMPTY case while doing your press setup, don't you?) in place and seat one of your bullets. It will almost certainly be too long, so turn the seating stem down a quarter turn and seat it again. Do this until you get to the OAL you want. Then take another case and do it again - sometimes pushing a bullet down in 4 or 5 steps doesn't produce the same result as pushing it down only once - and adjust as necessary.
I'm not familiar with the Pro 1000 (have used a 3-hole Turret and then a 5-hole Loadmaster for ~25 years) but if your press has room to use Lee's Factory Crimp Die I will strongly recommend its use. Makes adjusting the seating die a piece of cake, as you don't have to try to coordinate bullet seating depth and case crimp in the same die. Just set the seater stem to seat the bullet without worrying about any crimp, and let the FCD finish the round up.