Since I'm making sure that the PCs in my campaign are all the same level, how should I go about reading those level ranges in terms of appropriateness for my party? Should I take the median? So like, if an AD&D adventure says it's for levels 5-7, should I aim to use it at 6th level? If it says it's for levels 1-3, should I aim for 2nd level?
You can take the level ranges on old modules as fair for 5e, though for different reasons.
In classic D&D, classes had different exp progressions and multi-class characters split exp among their classes. So a 5th level multi-classed character might be every bit as capable as a 7th level single-classed one, or a 5th level Cleric or Fighter noticeably tougher than a 7th level thief. So part of the idea of a 4-7 or 8-12 module wasn't just that players might happen to have different-level PCs, but that some 8th level PCs might be equivalent in power and total exp to other PCs who were as high as 12th level.
In 5e, everyone uses the same progression, but Bounded Accuracy lets characters of differing levels work together fairly smoothly, still all being able to be challenged hitting the same DCs and ACs. At worst, the lower-level characters may be a bit fragile and under-contribute in terms of DPR.
Or, since many of these old modules were also written with 6-8 PCs in mind (were groups really that big back then?!),
I don't know if all modules were written with such specific assumptions, tournament modules may well have been. But, in general, yes groups could be pretty large back in the day, not just 6-8 but as many as 12. (Heck, I've run 12-player games as recently as 2011.) Player

M ratios had a lot to do with it. Games also tended, IMX to be longer, too, 8 hours or more. One local convention, started c1976, still uses mainly 6 & 8 hr slots, and a minimum of 6 players when scheduling most of its RPGs. It only just started taking 4hr RPGs with the introduction of 5e (something long overdue considering the 1-2hr Encounters format was popular for years before).
OTOH, I've heard that conventions on the east coast tended to use much shorter slots.
should I go for the top level? So if I've got an adventure that's for levels 5-7, should I aim to use it at 7th level since I'll have fewer than the expected number of PCs?
5e PCs have it a lot easier in some ways than classic D&D. There's no spell interruption, casting's more flexible, multiple attacks kick in earlier & hit easier, you get more out of your CON bonus to hps, etc, etc... Bottom line is a 5-PC 5e party can probably handle an adventure meant for 6-8 1e PC, if only because they'll have fewer rounds 'wasted' on whiffing or having the wrong spell 'memorized' or the like.
One exception might by Undead. Undead encounters could be pretty inflated based on the assumption of a Cleric Turning them, Turning is less dramatic in 5e and kicks in at 2nd level rather than 1st, and with Druids and Bards as otherwise workable 'healers' in the Cleric's stead, the Cleric isn't as
de rigeuer as it used to be.
So I'm really curious as to how this works. Do you use 1E monsters as is, or use them from the 5E MM?
I've had good success running 1e (AD&D) modules as-is, even to the point of not substantially changing monster stats (you have to invert AC for instance), but that was with very low-level modules. AD&D monsters would really want for hps relative to 5e as you went to higher levels.