I have been cubing for around 2 weeks and a half.
You don't need a new cube, work on the one you have. A cube you grow with will probably still be good down the road. Even though my storebought is still being torn to pieces by "better" cubes, it still holds up as one of my favorites, and I can get good times with it (~20 seconds, good for me). I have memories with the cube as well, it's not just the hot thing someone else recommended, it's a cube I had sanded and I really love.
I'm ranting, but the moral of the story is that you don't need a cube, work on your skills first, because you probably are still over a minute. You won't see much improvement with a new cube anyway, and you won't get that same bonding you would have with a new cube. In fact, figure out if you really want to cube anyway. Come back to actively posting in the forum later, learn some things, lurk, and you won't be a super noob. I know I waited until I was at around 35 seconds until I started actively posting.