IMO, you definitely want to import your Mass Effect 1 character into Mass Effect 2. All of the major choices that you made in Mass Effect 1 will be reflected.
For example, at one point you visit the council on the Citadel, and that plays out completely differently depending on whether or not the original council is still alive (same with the choice of who you nominated for the council, Anderson or Udina). The same goes for who you killed on Virmire (Ashley or Kaiden) and if Wrex is still alive.
The same is true for the side quests, to a lesser extent. However most of these only have the follow up in the form of an e-mail to your private terminal on the Normandy, but it's still cool to know that your choices had a lasting effect on the story.
If you had a love interest, it doesn't have a huge impact on Mass Effect 2. When you meet them, you share a brief kiss, but that's about it. You are free to have a new (different) love interest in Mass Effect 2, but apparently that will have some sort of impact in Mass Effect 3.
Bioware did an excellent job continuing the story you started in the first game. If you could make a choice in Mass Effect 1, it is reflected in Mass Effect 2.
As for importing characters, I'm not completely sure about this but I believe that you can import any play through for a given character (it's been a while since I imported my Mass Effect 1 characters). If you don't mind doing another Mass Effect 1 play through, I'd suggest starting again with your level 60 character (or whichever one you want to import), and make all of the decisions that you want to carry over to Mass Effect 2. You could always put the difficulty on easy to help things go faster.
If you want to know how a given quest affects Mass Effect 2, you can always check the Mass Effect Wiki.
If you don't import a Mass Effect 1 character, the game basically makes the big Mass Effect 1 choices for you. Also, some dialog that is present for an imported character is not present for a new character (mostly minor things, but some text wouldn't make sense if you didn't play the first game).
Finally, at the start of Mass Effect 2 you are able to change your class and physical appearance (don't worry, it makes sense in the context of the story). You can't change your sex or name, however.
I would definitely recommend playing the first game before the second if you can - the story is great and unless it's been accidentally spoiled, there are several twists and turns that make it really worthwhile. Just when you think you've figured it out and you think you're sooo clever, it'll surprise you :)
Though as you say, there is no Mass Effect 1 on PS3. There is however, a sort-of solution to not having a save game - there's an interactive motion comic that takes you through the major plot points and lets you make most, if not all, of the big decisions from the first game. The comic is included with the PS3 version of the game so you'd be good to go.
Btw, if you have a decent PC I'd recommend playing it on that instead. The graphics are better, the gameplay is a lot smoother because you don't have to keep pausing to use powers, and you still can't beat mouse + keyboard! :)
Best Answer
The easiest way to clean up your galaxy map in Mass Effect 2 with all of the downloadable content installed (as you clearly have above) would be to quickly go and scan all of the planets marked with minerals on them - these are adding up the bulk of the excess on your screenshot and won't take any time at all to clear (just planet scanning).
In the screenshot above, these are marked as the following;
I do not believe there is any other method of 'cleaning up' the galaxy map other than actually completing each thing listed on the map.