I've always liked that one mission in X-W Alliance, in which you have to identify a pretty huge Imperial convoy/fleet while dodging fighters, lasers and destroying probe droids in an A-Wing 
So in short: scout missions! 
Yeah, the original one of that in X-Wing was great fun too
Ahh the Warspite!
I think it would be almost impossible in FS2 without some modifications because one big point about scanning stuff in X-Wing/TIE Fighter etc. is you just have to get within a certain distance and have the thing you want scanned targeted.
In FreeSpace2, you have to have to 1) Be within a certain range, 2) Have the centre of mass of the ship or subsystem selected and in the centre-ish of the reticle and 3) Sit there like a sitting duck for 2-30 seconds.
So without change, the fast sweeping scan runs that you could do in the A-Wing would be a lot less fun (In fact, I'd rather take a B-Wing then because at least then you can survive being shot up while you sit there waiting for the scan to complete
)
As for Mission Ideas, I'd love for a little story on what happened to the Ram's Head Corvette and maybe something involving it's recovery and re-use.
I actually made a whole sequence of missions in XvTEd (Which was sooo much nicer to make missions in than FRED!!) but lost the lot in a disk crash about 11-12 years ago?
IIRC, it starts off with you on a convoy escort when the convoy picks up some signals from a nearby asteroid field. You and Red 1 are sent off to investigate and you scan a few things and eventually find the remains of the Ram's Head crashed into an asteroid (A certain amount of imagination had to be exercised here as IIRC I had to use container transports as asteroids or something
).
Everyone gets very excited and you're told to stay on station and guard it while recovery craft are mobilized.
But after a few minutes, predictably, the convoy comes under attack from pirates and you have to decide whether to go back and defend them. Whether you do or not, midway through the battle 3 Imperial transports jump in on the otherside of the asteroid field and make for the Ram's Head wreckage and there is a mission branch if the transports get away with the Ram's Head and you save the convoy, or you save the Ram's Head and lose the convoy.
Branch 1 lead on to searching, recon and an assault on a small imperial research facility to get the Ram's Head tech and data, while Branch 2 was you escorting it to, and then defending, a small Rebel base from imperial recovery attempts long enough for them to extract the tech and data before eventually legging it as it gets mobbed by ISD's and T/B's.
The branches then met up and then it was mostly running with the mcguffin while they developed something with it, although I can't remember what I was going to do there (Needed to check the timeline!), with some differences based on whether you saved the convoy or not (I think you had more missile, beam and ship choices if you saved the convoy, but if you lost it you were instead able to request reinforcements from the base (As it hadn't been blown to bits))
But all of the missions in XWing and TIE Fighter were inspired and incredibly well written, from the damned Redemption mission to the one where you get told to clear out a minefield on your own in an unshielded T/I, before being called a traitor and then having your wingmen and ISD try to blow you into dust and if you lived long enough the Secret Order sends an M/FRG in to save you from all the T/A's and gunboats!
Nothing in FS2 came close (Weell, maybe some of the SoC missions
), and it's only semi-recently with some of the third-party SCP campaigns that have matched their level
X-Wing Alliance was a big disappointment in that regard; The family missions were excellent but the rebel missions were so bland...
