If you have a Fuji, and its got a double chainring, you have what is called a loose ball bottom bracket that is square taper.
Yes the ball bearings are caged in a little cage, but it is loose ball. All Japanese bicycles from the 80s have these horrible bottom brackets except the very top of the line, because most of them used the funky external nut tightened, poor quality, bottom bracket.
The best thing is to get rid of that junk.
Third, your bicycle is too low of a model to dump money in. There is no need to change to a hollow type bottom bracket or a super new bottom bracket and cranks because you run into chain issues (width) and gear spacing and crank spacing. The strength of the new cranks is great, but square taper is more than adequate for any person who has ever used these forums and its been used by the best just fine (Le Mond) or (Merckx) etc.
What you do need is the right spacing. Generally you can go quite a bit more narrow than the giant size you picked. I recommend a 110 for double and 113-114 for triple.
The all in one units like Phil Wood are all about the same really for your purposes. You can get a great bottom bracket for $25 these days in a sealed unit square taper.
The average bicycle poster seems to have large amounts of money I find and considering your bicycles other parts, its not worth dumping anything modern or excessive into, except the great 700 x 28c wire bead (non tour guard) Pasela tires and a nice solid 7 speed chain. with a traditional bicycles you are not missing much like the geeks would have you think. The old bicycles were wonderfully tough and rode well with little investment. They also didn't have racing dimensions for bicycles that get used by people who want to just roll around and enjoy a nice ride.
The new cartridge units are a narrow stance on the bearings and that Does make a difference and loads are not only horizontal or vertical on bicycles you must remember. This flex is not enough to out weigh the ease of installation and good quality seal they all have.
Tighten your cranks tight, then come back after your first ride and tighten again. Also go a tad bit tighter on your bottom bracket than the recommendation and you will not have to go back later and adj. again.
Oh and also...re bearings...smaller bearings are better.. The closer the inner ID and the OD of the races, the less sliding the bearing has to do. Bearings always slide some when surfaces are different diameter. Think about it. There is so much false information out there. Look at roller bearings ... they are tiny bearings ... Good luck. $25 is all you need.