Classic or skate: where I would start again
When I started, I rented skate skis because they looked faster. Two weeks later I was back at the counter asking for classic gear. Here is what I would tell a friend who is about to buy a first pair.
Classic is the honest teacher
Classic technique is the diagonal stride in tracks: kick, glide, repeat. The tracks keep your skis pointing the right way, and the technique rewards balance on one ski more than raw strength. If you can walk, you can ski your first kilometre on classic skis the same day.
The catch is grip. You need kick wax, a skin insert or a fishscale base to stop sliding backwards. Getting the wax right is a small craft in itself, which is why I wrote a separate cheat sheet.
Skate is fast, and honest in a different way
Skating looks like ice skating on a wide groomed trail. No grip wax, only glide wax, and the speed is addictive. But it punishes weak balance and poor fitness immediately: on the first uphill you find out exactly how strong your hips are.
My rule of thumb: classic first, skate in the second season, both after that.
What I would buy today
A pair of classic skis with a skin insert, comfortable combi boots if the budget is tight, and poles roughly up to the armpit. Rent skate gear a few times before buying it, and take one lesson. Twenty minutes with an instructor saved me a whole winter of bad habits.