An HBO/AMC series in the style of something like Game of Thrones would be awesome. I think the best place to start would either be the Grey Death Legion story or the 4th Succession War. If it were a story about the GDL it would have to focus more on the Mech combat, which would be cooler but also more expensive and overall less appealing to the audiences were trying to reach, but it could still work.
I'd rather see a darker reimagining of the 4th Succession War though. Reading the
Warrior trilogy felt like 3 books worth of Mary Sue fanfic and there's just too much good stuff in there to be let down like that. There's a secret alliance (sealed with the marriage of a 45 year old "king" and the recently turned 18 "princess"), a longshot scheme to get double agent Justin Allard into a position of prominence in the Liao (who could really have their crazy played up) intelligence agency, duplicity by ComStar who profess to be the neutral party, and so much more.
I'd see the series work a little like this:
Season 1: Focus on Justin Allard's apparent fall from grace and rise to prominence on Solaris. The idea that Justin was in on the scheme the whole time is kinda lame, so the exile should be "real" and Justin can have a great big sob about it. Cut to Solaris where he's doing the only thing he knows, blowing up big robots. But intrigue is afoot on Solaris and house spies are always trying to recruit new blood...
The second focus of the season would be on Hanse and his secret plans for a Steiner/Davion alliance and attacks on Liao. He knows someone is feeding Liao information on troop movements but not who, and we can see some ComStar mediated debates between him and Katrina Steiner as well as some budding chemistry between the Fox and Melissa.
Third main focus is on the Wolfs Dragoons helping Minobu Tetsuhara build the Ryoken. This part pretty much writes itself, and needs to be told alongside the rest to set up the conclusion...
The Davion-Steiner wedding, which would be the season finale. We see Jaime Wolf barge in with Minobu's swords and insult Takashi, ComStar has some meetings about how the Federated Commonwealth alliance will be bad for them, either Hanse or Quintus can apologize to Justin and offer him a place back in the Federated Suns, and the episode closes on "My dear... I give you the Capellan Confederation."
Season 2: Will have things like Takashi gunning for the Wolf's Dragoons on the Davion border, Melissa Steiner's kidnapping and eventual rescue, Justin trying to decide which side he belongs to, and we can get some crazy Liao scenes.
Season 3: Unless someone can think of a way to really drag this out, you'd see the end of the 4th SucWar (yeah I just did that) as well as the introductions of the new generation of leaders. The timing here might need to be fudged (either by long jumps to the future or messing with the accepted timeline) because if there's gonna be a fourth season it should be the clan invasion.
The hardest parts about making a series like this would be selling it to a network; a well written book or comic series is a much easier sell than poorly written game lore, and the effects; Mech battles would have to be entirely CGI. The best bet for an effects studio would be the one that BSG had since they did top notch effects on a cable TV budget, and they got the industrial sci-fi military look down really well.
PS: If nothing else, writing a hypothetical series bible for this would be fun!