Howdy Xeathos, welcome to Freelancer.  In single player there is a set story line to follow, with options to take little side-quests along the way and do trade runs as well. Vanilla (stock FL with no mods) ends around level… hrm 20 or 30? (been a while) It’s a pretty cool story by itself, but after you finish that the side-quests are pretty much the only quests you’ll do in multi-player. One side-note, only in single player can you do the full storyline.
But there is plenty of fun to be had in MP with so many mods out there; new ships, new star systems, re-done graphics, better AI for NPC’s, hire-able wing men, jazzed up effects, custom music and sound / voice, custom factions, and almost every one changes their trade routes and goods.  For me some of the most fun was just exploring and finding new items or new foes. But the PVP can be verry fun too >:) As others have said, its physics are not like regular space flight. Which gives the possibility of flying ships that handle like mad, or trade off a little and haul bunz, or have a crazy load-out. The other cool thing in MP is that most enable Capital Ships for player use, and up the cash limit to ~2 billion.
Anyhoo, you’ll want FLMM -freelancer mod manager- to get mods installed. Extensions are .flmm which are either a zip file, or 7zip (usually that will be in the file name, if it’s 7zip you want FLMM 1.4, otherwise stick to 1.3).  There should be a getting started thread around here listing all the updates and global server work-arounds to get you up and running. That last one is handy because Microsoft finally pulled the plug on their server listings, so the community had to come up with their own solution. Many servers also list how to connect directly via making a shortcut with the server IP as a switch. It might sound like a lot, but after you’ve done it once or twice it’s pretty easy after that.
Good luck, and good hunting 😃
EDIT:: woops, almost forgot! Very important, be sure to write down your multi player ID for backup, if you re-install that number will change, and it is how your characters are stored on all multi-player servers. Look in the \Freelancer\EXE\ directory, double click myflaccountid.hta and thats what you’ll need to write down.