you can't go wrong with any of these towns. seriously, pick the nicest home you can find in these communities, since all of them are well-regarded, family friendly, and have great schools. with your budget, you won't have a problem finding a nice home anywhere in the area.
norwood and old tappan are part of the same school district, so the kids from both of these towns (as well as harrington park, northvale, and rockleigh) attend the same high school. demarest shares an equally good school district and high school with closter and haworth. northern valley regional high school at old tappan and northern valley regional at demarest are big-time rivals in academics and athletics, but the truth is they're really similar in many respects.
in terms of prestige, i would say that old tappan and demarest are tied at the top and norwood is a half notch below. but again, all of these towns are considered nice.
all three towns have a mix of middle class, upper middle class, and upper class residents but are considered wealthy overall. the difference is that norwood has a larger middle class population, which is why its overall income level is not nearly as high as the other two towns.
all three towns have very similar levels of diversity - mostly non-hispanic whites with a sizable minority of east asians (around 25% - mainly koreans). the local public schools in these towns are over 30% east asian, i believe.
check out
SchoolDigger.com for more specific information about school rankings, test scores, and demographics for the elementary, middle, and high schools that interest you.
one negative about these towns is that they don't have much of a traditional walkable downtown area. old tappan's downtown consists of some strip malls with a large supermarket while norwood and demarest have small, modest downtowns with only a few basic amenities. most residents of old tappan and norwood go to neighboring northvale for their shopping, since that town has the largest commercial business district of the old tappan-adjacent communities. incidentally, northvale is the least affluent and least prestigious community in the immediate area, with the largest percentage of blue collar and lower middle class residents, although it's hardly undesirable; it's just that it stands out for being unremarkable in an area with some very desirable towns.
meanwhile, demarest residents tend to go to neighboring closter for most of their everyday shopping needs, since closter has arguably the largest and nicest CBD in the northern valley, with a traditional walkable downtown area, a small movie theater, plenty of mom-and-pop stores, etc.
if i were you, i would also take a look into the other towns of the northern valley, such as closter, haworth, harrington park, rockleigh, cresskill, and tenafly. all of these are terrific family-friendly towns with great school districts (tenafly and cresskill each have their own separate, highly-ranked schools). tenafly has an excellent walkable downtown that rivals closter's and has a lot of town pride in general. it also offers a slightly quicker commute to downtown manhattan than any of these other towns.
the only downside is that most of these towns have high taxes. that's one area in which haworth and tenafly in particular are notorious. not sure about the taxes in demarest, norwood, or old tappan. rockleigh is supposed to have very low taxes and has a lovely, semi-rural feel, but the housing stock is very limited.