Also, one of the things you shouldn't do is play for ranks... aim to beat your own scores bit by bit rather than those of others. For about a year my school's firewall blocked osu!'s connection, so I just played offline and measured myself against my own high scores. It's a much better way to grasp the game and your own capacity, and there's no point trying to compare yourself to veterans/etc.
As for improving on certain maps, you can watch a replay or maybe have the Auto mod play it for you and look at the parts where you screw up. Sometimes a pattern is confusing and hard to follow, or you just lose rhythm, and this helps you understand what's going on and what you're missing. Playing the map on Half-time can be a bit boring, but helpful in the same way as the above. I wouldn't recommend the Easy mod, as most of the time it actually increases difficulty, i find, especially on maps with lots of notes.
Some of the old beatmap packs have maps that are somewhat more difficult for all the wrong reasons - small circles, etc. - so I would honestly just recommend browsing through recently ranked/most played/highest rates maps. These are often much more playable and much more enjoyable. Moreover, as has been stated, every mapper has a different style and thus a different scale of difficulty within their mapsets. To get a more accurate understanding of your current skill level you should branch out and play a huge variety of maps. Don't take the star rating system to mean too much outside of a rough scale. One mapset's 5-star can be inexplicably more difficult than another's, and you should try the harder difficulties yourself in order to get a grip of what you're comfortable with.
As for improving on certain maps, you can watch a replay or maybe have the Auto mod play it for you and look at the parts where you screw up. Sometimes a pattern is confusing and hard to follow, or you just lose rhythm, and this helps you understand what's going on and what you're missing. Playing the map on Half-time can be a bit boring, but helpful in the same way as the above. I wouldn't recommend the Easy mod, as most of the time it actually increases difficulty, i find, especially on maps with lots of notes.
Some of the old beatmap packs have maps that are somewhat more difficult for all the wrong reasons - small circles, etc. - so I would honestly just recommend browsing through recently ranked/most played/highest rates maps. These are often much more playable and much more enjoyable. Moreover, as has been stated, every mapper has a different style and thus a different scale of difficulty within their mapsets. To get a more accurate understanding of your current skill level you should branch out and play a huge variety of maps. Don't take the star rating system to mean too much outside of a rough scale. One mapset's 5-star can be inexplicably more difficult than another's, and you should try the harder difficulties yourself in order to get a grip of what you're comfortable with.