This thread covers an awful lot of issues -- page size, page publishers, acid-free or not, and so on.
Acid-free paper is essential, I'd think, of some variety. There are de-acidifying sprays which might help to control the problem, but that could get very expensive very fast.
Weight of paper is important, too. The paper weight of 20# ("pounds") was mentioned, but that is the weight of normal computer printer paper and is much too light for mounting large numbers of stamps -- and will surely tear as you turn the pages. Although paper that is as heavy as 100# works fine, that weight has always seemed too close to "cardboard" for my taste, so I've settled on the weight used by most album publishers which is around 50-60# paper. I find a lot of 65# paper at places like Staples, but I've only seen it in 8.5x11. It's sturdy but not overly thick.
Print shops can supply good quality paper to match exactly what you want, and they are not overly expensive, I've found. Take a sample page so they can match the weight, color, and size. They'll find good quality acid-free paper that matches or nearly matches and can make you huge numbers of blank pages, all cut and hole punched, for not as much money as you might think. I've found that punching round holes is easy for them, but square or rectangular holes (Scott pages) are a bit more difficult to do.
You could buy thousands of these pages all ready to be printed on for less than buying pre-printed album pages. I find it useful to remember to compare these prices to high quality already-printed album pages and not just to reams of office supply paper which is always very cheap.
Color. Bright white or "cream" colored is worth considering as you're not going to like it if you decide much later that all your pages are really too white or too dark.
Printers print on 8.5x11 paper but "wide bed" printers will print on larger album-page pages easily. Additional expense, of course, but a one time purchase (hopefully). You want to buy a printer that feeds straight through rather than one that curves the page around, to avoid curling, bending, paper damage, smearing ink, etc. You can print on Scott album sized paper (which is sold completely blank from some vendors--Subway Stamp Shop might be one?) and perhaps on others, too.
The album page program you showed page examples of is a direct copying of Scott Specialty pages, unfortunately. It would be kind of nice to be able to print Scott pages onto your own paper -- much cheaper than otherwise. Someone did a little "borrowing" to produce that CD or website, I imagine. I wonder where it came from and who published (borrowed) it? I imagine someone is selling that on
ebay in competition with the many other programs for printing your own pages now sold.