You can try HR (and definitely HD), but you want to do it at the 2* range. I am not sure if mods would help or hinder development at your skill level, but you can see if it does.
You should play as many different maps as you can possibly find. Train consistency for the most part and have a "passing practice" session every few days. You probably want to do no-mod until you reach 5 digit. Make sure to direct your focus to each circle for now (you'll get better and further develop your focus on your own and properly). Lastly, play to the beat (I know this is hard to do at low difficulties, but it will help immensely later on).
You should definitely play for PP (which doesn't necessarily mean "farm PP"). It's a great external motivator for improvement and, for the majority of the player base, PP is an accurate indicator of skill level. Playing for PP also enforces consistency, which is the differentiator between you and others around you in skill level. But most importantly, HAVE FUN. You will go much further ahead in the long run having "fun" (whatever it means to you) with the game than over-stressing trying to get better at it. It'll also probably end up very destructive...
Albeit you must have fun, don't have too much fun. If you really want to improve fast, you'll have to discipline yourself and play a certain way that's most optimal for improvement. Training to be consistent can be VERY frustrating, so to offset this you should try playing multi, playing for passes, trying some new mods, mapping, or anything else that makes you feel good--except playing way above your difficulty threshold. NEVER do that -- it's like the osu! equivalent of drunk driving but instead of killing yourself, you're killing your improvement gains (not to mention that you WILL get addicted to it and not want to go back down to the lower levels despite you passing firetruck all). All in all, you have to find a good mean between having fun and playing seriously.
Sorry for the long-winded post. Just wanted to get the last idea out there.