I've never played this franchise before and I'd love to give it a shot but I don't know if I should start at the first or just skip to the second. I assume these games aren't story heavy so I imagine skipping to the second would be the smart move but maybe the first has stuff I'd miss out on. What do you think?

I would say, look for some gameplay videos and see which one you prefer. It's not that the second game is better because it's newer. The second game is almost as old, and has no pretty graphics in the slightest. Some people really prefer DK1, others like the sequel.

The first game was a huge experiment for the developers, a true project of love even, which eventually had to be rushed to a finish line but it has lots of charm and nice details. It's light on content, basically a single - but good - campaign and 15 separate levels, but the gameplay is very nice. Building a dungeon just feels right, but there's a good chance that after that you're done.

DK2 featured some improvements in the areas the first game was lacking(workshop, mana), but it was a quick cash grab and a rush job, and it shows. Where the first game features an imaginative cast of heroes and evil creatures, the second one is mostly humans on both sides, and in some cases even the same unit on both sides in a different color. Dungeon building is not as nice, unit's hardly have any skills( A wizard goes from 10 to 2 abilities for example) and the campaign is not as good.
However, DK2 does has a more or less working multiplayer, a 'pet dungeon' feature, animated cutscenes and some skirmish maps.

i would suggest playing the first, gameplay is overall faster paced, more monster creatures like Dragons, Hell Hounds instead of humanoids, and imo has more personality than the 2nd game, better humor, more stable than running DK2. more indepth here: https://keeperklan.com/threads/5435-Why-DK1-is-better-than-DK2

you can opt to use keeperFX for widescreen resolutions instead of original dosbox version that comes with GOG.

1) Install Dungeon Keeper GOG
2) Download KeeperFX
3) Extract KeeperFX
4) Run the launcher.exe from the KeeperFX folder
5) Press Install and navigate towards the GOG folder to install KeeperFX
6) Change the screen resolution in the launcher to something that resembles your own PC.
7) Copy the music files from the GOG folder to the KeeperFX folder, and in the launcher from 'Run Options' select 'Music files instead of CD' to have the music play.
8) Click 'Start Game'

As Loobinex said, just take a look at how both look and play and make your own decision. It really comes down to taste.