Among fountain pen users back in the 1960s, when ballpoints were starting to take over, Parkers were considered a decent but not special brand, they mostly had steel nibs instead of gold and usually had aluminum or hard plastic barrels, so they were less delicate than pens made of natural materials such as bone or wood, and were indeed a popular gift for high school students. You can always spot them because the pocket clip is shaped like a stylized arrow. The plastic cartridge design was a new innovation started in the early 1950s. Parker fountain pens are still widely available (and they make plenty of refillable ballpoints as well.) Just search "fountain pens Parker" on
Amazon; you'll find a wide selection at several price points, or you can usually find some in stock at any good office supply store. They are definitely nicer than semi-disposable plastic pens that you can buy in a multipack this time of year.
My Dad was a bit of snob about fountain pens, and we all learned to use them. I regularly used a fountain pen up through high school, but once I started working I needed a pen that could handle carbon copy forms, so I pretty much gave them up, except for special calligraphy projects. The favorite brand in our house was Schaeffer, and always, always, a model with a gold nib. (Gold nibs are softer; they create a much nicer line and are less likely to accidentally puncture the paper, especially if you are writing on onionskin paper, which we usually were for correspondence, because we often sent letters to family in Europe.)
I still like fountain pens; they flow very nicely, and I usually use them for things like Christmas cards where you want the penmanship to look as nice as possible. I'll warn you, however, that they can be difficult for left-handed writers, because the ink tends to dry more slowly than ballpoint or gel, and you have to be careful not to smear it with your hand. (My DH is left-handed; he hates fountain pens for this reason.)
Cross ballpoint pens had become the usual American "special" pen gift by the mid-1970s, and it was common to have them engraved with a name or monogram. Cross' big style trademark is an extra-slim barrel design, and they became especially popular with women for that reason. I've received several of them as gifts over the years, mostly from employers, though I did get them as gifts for my Confirmation and my high school and college graduations as well. (They made wider-barrel models, but the slim ones are probably the most commonly gifted.)