OK, if y'all didn't know this already,
SPOILER SPOILER SPOILER!
Mystery Man,
I'm dividing my post into two parts: Mechanics and campaign development.
Mechanics
There are some conversions floating around; take a look on this site under the Conversions link. I've done my own (much more detailed) conversion, but it's not OGC and as such I can't post it under that forum.
In general, the ELs in G1 range from 7-11 using a straight conversion, making the module (IMHO) appropriate for 4 9th-level PCs, or a strong, stealthy, or cohort/animal companion-laden 8th-level group. The Great Hall is MUCH tougher, especially if you give the chieftain and his wife class levels. However, it is my opinion that even in the 1e version, the Great Hall was never meant to be the site of an open battle; no 8th-level PC party could have deployed the firepower necessary to take on 20 hill giants!
The big problem, IMHO, is the sudden jump in ELs between G1 and G2 (assuming you go that route). While G2 and G3 have a relatively smooth EL progression even if converted in an encounter-for-encounter fashion, G2 really requires an 11th-level party to survive it, and probably works best with a 12th-level party, unless you seriously reduce the number of giants.
Finally, there are the dragons. Simply put: Rewrite the dragon encounters entirely. I'd even consider substituting other monsters; IMHO, there are just too many dragon encounters in existing modules to add more.
Campaign:
As with most EGG modules, G1 was originally written for tournament play. However, it's easy to jazz it up for your campaign, especially given how well the module dovetails with the official line on the Silver Marches. I'd suggest the following:
1) Strongly consider NOT running G1 as a standalone. It has much more flavor if you put it in the context of the other modules in its series or, perhaps even better yet, the entire G/D/Q supermodule!
A big problem with G1 is that the principal adversaries therein are, of course, hill giants: big, dumb, straightforward monsters. The intrigue to G1 centers on the forces controlling the giants rather than the monsters themselves. So a key thing is to play this up! Focus on the non-hill giant NPCs in module. There are stone giant emissaries, perhaps trying to plead diplomatically with their lesser cousins to cease their fierce hostilities against the Silver Marches. There are potentially disgruntled bugbear, orc, and ogre slaves, who perhaps seek to overthrow their larger masters. There is the cloud giant emissary: What's he doing there? Perhaps he's being recruited by the force motivating the hill giants, but seeks to take direct control for himself.
2) Whether or not you run G1 as part of a series, a motivating force is critical. One option, that would work quite well IMHO, is to use Gerti Orelsdottr (and, if you want to get REALLY nasty, her circle of frost giant runecasters) as the BBEG(s). You then could consider running G1 (set in the Crags, perhaps, or just deep within the Evermoors), then have an interim adventure during which the PCs travel north to the Spine of the World and lands beyond, wherein lair Gerti and her compatriots; the Spine is notoriously dangerous, so encounters with everything from stray forces of Obould's to "madbeard" insane dwarves could be possible. Eventually, the party could arrive at a modified version of G2, to fight their way through frost giants and cold creatures to Gerti's lair. (Note; Gerti is, by 3.5 MM standards, a CR 13-14 encounter; you might consider either boosting her levels a bit or giving her some runecaster support, or both, depending on party strength.)
Another option, of course, is to use the structure in GDQ1-7, which really does work quite well in a Silver Marches context. (After all, all the parties concerned do hate the Marches!) If this is just too many giants for ya, consider cutting out most of G3 (it's difficult to place fire giants in the North, after all) and adding Level Two of G3 as an additional level to G2 (replacing all fire giants with frost giants, of course).
3) Keep in mind that in this sort of module, it is paramount to have dynamic rather than static encounters. The major problem with G1 at first glance is that it seems to follow a tedious pattern of "open door, see giant, bash." However, if you run the Steading as a living, breathing entity, and move giants around the place as though they actually lived there, it becomes easier to deal with. This also has the advantage of allowing you to cut down on the sheer number of giant encounters; assume that many of the giants are out (on raids for instance), that at least some of the 20 giants encountered in the Great Hall live elsewhere in the Steading, and that their rooms are currently vacant rather than occupied by still more giants, and that the place is alive with slaves scurrying around on tasks (and full of gossip and information available to the party with the right spells!), and you'll have a place in which the players will be really excited to snoop about.
4) IMX, the best storytelling in this module will come about from the players' own decisions. I've suggested some NPC motivations and interactions that you can play up; however, some more possibilities are suggested by the following:
-Dressing as giant younglings: If the PCs go this route, they can have some very interesting interactions, especially with the giant matrons.
-Slave rebellion! If the PCs are smart, they may try to rile up the disgruntled slaves against their giant masters; this actually happened IMC!
-Prisoners: Prisoners are always fun. The unknown NPC dwarf in the forge area can be fleshed out nicely to make for a great NPC.