A lot of what you should work on depends on what level you are currently at. But since I don't know this, I'll throw you a general idea of what you should be getting done.
First of all, there is a large array of youtubers who can help you depending on what level you are at, but for this I'll just link the ones who are established in the competitive scene (all of these will be at least ESEA Main players)
voo csgo
Mauisnake
teamblight (although most if not all of these videos are done by flashstep, their igl)
boomeo has a huge library of videos by pro players, and if you like them enough you could subscribe to their website for even more.
So, watch some of their videos when you have the time, but not all at once, or you won't actually apply them to your game.
Next, let's talk about your binds. I have not seen many competitive CS players who uses their scroll wheel to cycle through their weapons/nades. I would recommend making separate binds for each of your grenades. (for example, I have my flashbang bound to F, HE Grenade bound to X, smoke bound to C, and molotov bound to Z) This will speed up the process of switching to a grenade, and eliminate the chance of scrolling past it or whatever.
Peripherals are also pretty important, but only to a certain extent. Get a big mousepad and lower your sensitivity. Bring it down to somewhere in the range of 2.0-3.0 @ 400 DPI. The lower your sensitivity, the higher your accuracy will be, but if it gets too low then you won't be able to flick/react as well. The general rule of thumb is to be able to do a 180 from the middle to the edge of your mousepad. You say you have a bad mouse, so I'd personally recommend investing at least $60-$70 into one, because it really matters. There's this amazing youtube channel,
Rocket Jump Ninja, who does mice reviews. I'd recommend looking through the zowie, logitech, and maybe steelseries/razer mice, just to find what really fits you. Personally I love my wireless G403, and
it's actually 50% off at BestBuy right now (if you end up getting a good wired mouse, you should also look into getting a
mouse bungee). Your keyboard can be whatever, but a mechanical one is preferable. And your headset should be decent, but you don't need to go overboard with it. The HyperX Cloud II's are amazing for their price, and if you have some extra $$ then you should look into getting some Sennheisers. And last but not least, you should look into getting a 144hz monitor. Not having one puts you at a disadvantage vs those that do have one, and having one will put you on equal grounds, or give you that advantage vs those that don't have one.
That's all I'm gonna post for now, but if you want some more advice then feel free to pm me or add me on steam.