First of all, kit makes no real difference (for us amateurs)... ok, you might be doing a bit of stitching if you want to shoot "conventional" landscapes and you only have a 150-500mm zoom but that's probably an unlikely scenario
With a kit lens or even a prime or two, you can take almost any style of photo you want, perhaps apart from birding or motorsport (and even than you can still approach and have a bit of a play at the fringe).
I took up photography first of all about 10 years ago with an old film SLR and then eventually a DSLR. I fell out of love with it pretty quickly, because I wasn't taking photos that interested me. It's only been that last 6-7 months that I've bought a new (well to me - it was 2nd hand) DSLR and a couple of lenses and really got back into it again. The reason? I have kids, I enjoy hillwalking and I want to take photos of these things. When I'm looking at my photos on screen, I'm smiling because I genuinely love the subjects I'm looking at (maybe not quite so much when they're bug shots
).
I found for a while I was taking a LOAD of people shots - well, specifically my kids. To be honest, the shots were pretty rubbish, technically, but I liked them because of what they recorded and showed me. The only way to improve your photography is to get out there and take lots of photos - reading books and watching youtube will help accelerate it, but there is no substitute for experience and learning from mistakes. To do this, you really do have to want to and have to enjoy it. So taking photos YOU like is good! The more you like it, the more you'll get out there.
Sure, there are different skills involved with taking a landscape or a portrait but ultimately both are about capturing light in an emotive way. One might require a bit more interaction with the subject, but the technical process of using the camera and instinctively knowing what your settings should be are somewhat common. So absolutely do focus on taking pictures and focusing on a genre which appeals. If it helps grow your passion for photography than that's a great thing. At some point, you may find you want to widen your photographic approach or interests, but it's your hobby so it's whatever YOU want to do. Don't ever feel like "ooh, I haven't taken a landscape shot this month, I must get out there and do it" unless you genuinely want to. If your hobby starts to feel like a chore than you're more likely to lose the love for it.
I would add that your rate of improvement will probably tail off as you develop your skills (learning curves are steepest at the beginning), so you may find you WANT to try different genres, techniques or subject types after a while... because you're not seeing as much improvement as quickly as you'd like. I'd always urge patience, but switching genres can get you back to "beginner" again in something else and as I mentioned earlier, getting out and taking photos should be your aim, so if that's what you want to do, then that's your call. I personally found being a complete beginner again (e.g. having a go at macro this week) was great fun and my rate of improvement certainly went through the roof. It also gave me a slightly different appreciation for some of the technicals - more subtle lighting control, manual focus, tiny apertures etc.
But find what works for you. And don't ever let anyone tell you that the way you enjoy photography is wrong. Because it isn't.
Right, I need to get out to take a landscape shot or two - that's why I'm up at stupid o'clock!