After your starting planet, you will indeed meet up on Coruscant. Your class quests are indeed individual, but they do have a similar track record.
I will try to explain this as easily as possible:
Each planet is usually divided into sections. These sections can be identified by the binding points for travelling and/or the Taxi Access Terminals. All of the class quests follow this logic.
With that in mind, you and your friend can easily level together in the following manner:
0. Make sure you are grouped.
1. You both arrive on the planet at the same time.
2. You both go to your respective class quest giver on the planet.
3. When the quest has been given, you meet up again.
4. If desired, pick up other quests together (the triangles on the maps are quest givers that everyone can access).
5. Check your map: You should be able to see both your missions as well as the missions of your partner (if you are grouped). Notice how they are usually not in the exact same location, but they are on the same section of the map.
6. Go do all the quests that are on the map. Both you and your friends should also help each other with your respective class quests.
7. When all quests have been done (note: each mission will say something like "Return to xxx" or "Speak to xxx") go back to hand in all the quests you have fullfilled. (note again: on the map, your quest givers will now show as a triangle with a green center).
8. You have now finished a section of a planet together. Your class quest will send you to your next section, and usually, your partner will receive the same kind of message in his/her class quest.
9. Do the same for the next section :-)
As for your Level 33 friend. Don't let him group with you unless you are Level 30+ as well. He will seriously gimp you and your friend in the following ways:
- If you group with him, your experience gainings will be significantly reduced, meaning you will very soon be underleveled for the content, and he as well as he's not gaining any experience.
- If he keeps on destroying all your enemies and you do nothing, by the time you're 30+, you will have no idea what your class can do.
Good Luck and if you have further questions, don't hesitate to ask.
I'd like to add that this post is very well written and full of excellent information. If we could vote on great posts/replies you would have my vote +1. This contains everything I would have replied with and more!