I owned DKC1 as a kid and rented DKC2 and DKC3. I didn't like the second as much because it was a lot harder, but I loved being able to fly with Dixie. I loved DKC3 because it was easier, and (admittedly) a lot more kid friendly with its brighter colours and cartoony enemies. However, playing them later in my teen years, I've grown a much stronger appreciation for DKC2.
DKC1 has awesome level design in terms of atmosphere, and I'd have to rank it slightly above DKC3 (though below DKC2) in that aspect. It probably has the most variety visually, but gameplay-wise it doesn't hold up to the other two in my opinion. I love looking for secrets, but in the original, it just felt like hopping down random holes.
DCK2 brought a whole lot of concepts that were missing from DKC1, like a lava world, a Gang Plank Galleon world, being able to climb, the concept of bonus games and not just bonus rooms. The difficulty was brought up and the collectables were introduced magnificently imo. There was enough to keep me coming back, and even without the hidden coins and such, the levels were fun enough to play on their own. I still play the game through once in a while.
DCK3 is a close second for me now. While it certainly has a lot more variety in terms of gameplay, sometimes it actually felt like a fault to me. When I wanted to play a really fun, challenging level at a certain point in the game, I'd get a Rocket Ride, or something where the controls were inverted. It's something that's easiest to appreciate in a first-time playthrough when it's unique. After you've completed the game and mastered all the game's tricks, it's not a pleasant surprise but more of a let down in a way. The game is still great, and I agree with almost everything else that's been said about it, so don't get me wrong- It's not often that my only complaint about the game is that there's a lot of variety!
If you want a straight platformer with great level design and lots of secrets, I'd recommend DKC2. If you want an innovative 2D platformer that mixes up gameplay styles, I'd recommend DKC3. If you want to play the DKC series, I'd recommend playing DKC1, because I find it hard to go back after playing its sequels.