OK, i've run a bunch of Mechwarrior RP games and BT games over the years.
There are a few MAJOR challenges.
1: So, I've got this Gauss Rifle....
It can be very difficult to maintain anything that even remotely looks like game balance when players have access to immense firepower at character creation. The scale between what a character with a mech can do and what a character without a mech can do is so large that they can't really even be compared. It's like Zombie Andre the Giant and Stephen Hawkings getting together for a sumo match. So the challenge becomes comming up with plausible reasons as to why the players have to get out of their mechs.
2: Sorry, but I've got work tomorrow...
BT games aren't know for being quick. Even just a 4 on 4 match with 4 players vs a GM can take a couple hours to play out (longer for new players) and requires a fair amount of prepwork in maps and recordsheets. Unless your the All-Day-Saturday type, you probably won't have time for much else on a typical game night.
3: You put points in what?
It can be difficult to convince players that they have to put points in things other than their mech skills. If every player becomes a master carpenter, then most of your NPC will start to look like nails. It can get pretty frustrating to be a GM with a neat new NPC you want to RP, when the players decide to hit his house with a couple of LRM salvos at 2am.
Over the years i've tried a few differnt techniques to handle these problems. I've generally prefered to go one of two routes.
Either each player makes 2 characters, (one for in Mech combat, and one for out of Mech combat) or we just go easy on the RP side.
The first option give the GM flexibility in designing adventures that won't kill Mech pilots on the ground, or make somebody's super-spy character into humanoid-ish grease stain on a battlefield. I haven't actually done this one in a couple of years. Most of the time, if my group wanted a fair to large amount of RPing, i went with a different system. Sure, there is a good set of rules that will allow you to run a decent RP campaign in the BT universe, but for me BT is all about the mechs.
The second option is the one i go with no, even when i play online via MegaMek. I use my own house rules to stream line all the RP aspects of running a BT campaign, and focus on the glorius mech on mech action. I'll give you a quick run down on some of them.
At what you would normally call "character creation" I put the players in charge of unit creation. I grab which ever one of the Mercenaries books is closests to the top of my pile at the moment, and divide up the points between each player. Then each player either picks, or is assigned a unit "role". Who ever has a specific role has to use his part of the points (C-Bills, or whatever your using) to acquire assets that will help him accomplish his role, in addition to whatever share of the fighting force he wants to be responsible for. I make up the roles each time based on the number of players I'm going to have.
Here is how one of my current groups is broken down as an example. (names have been changed to protect the guilty)
Alfred is the unit Commander. The unit commander is responsible for EVERYTHING, but primarily responsible for nothing. He's allowed to assist with any operation, but, (despite his title) doesn't have final say in much except wether or not to take a contract. Alfred started with a lance of medium mechs, enough techs to support it (barely) a couple of scouts/agents and a transport helicopter.
Buford is the units Recon/Intel officer. This gives him final say in deciding what the scouting priorities will be, as well as handling any RPing for information that happens. He's started out with 3 lights and a medium, along with enough techs to do basic maintenance on them. He also runs 8 scout/agents, and a pair of light scout vehicles that help with comm relays.
Cletus is the Line Commander. He's just in it for the Big Guns. His only part in the decision making process is the allocation of captured/salvaged/purchased mechs and hardware. He started out with 2 meds and 2 heavies, along with enough techs to keep them running, and take care of most battle damage.
Dingus is the Support officer. He determines priorities when it comes to repairs and supplies. If the unit runs out of SRMs before the final fight, it's his fault. If somebody's mech isn't up and ready to go, yup, it's his fault again. He's also in charge of the actual contract negotiations (within limits set by the commander) He started with 3 meds and a light, and more techs than you can shake a stick at, along with a couple of flatbed trucks.
To make this game work, I had each player assign a priority (A through F) to each of the 4 positions (which then became a Skill Strategy, Recon, Tactics, and Repair) as well as Piloting and Gunnery. A got a 3 for a target number, B a 4, C a 5, D a 5, E a 6 and F a 6. The rest of the players units were given standard "regular" ratings, and no additional skills.
Everything that can't be resolved with a quick bit of RP, is handled by one or more quick die rolls. Everything outside of mech combat is kept quick and abstract.
At the end of each session, i assign Exp to each person based on how well they accomplised their respective rolls. This means that even if my Tech officer kills a Victor with a Commando, he won't get any bonus Exp for it, but if the Commando was the only mech in working order for that fight, he'll get a penalty. (Poor Dingus

) Skill advancement is a simple point system from one of the books ( i forget which one it's in)
If one of the players dies, his position becomes open for any player who wants it. If more than one wants it, then it goes to the one with the highest applicable skill. In the result of a skill tie, the one who put the highest priority in it. If it's still a tie, I accept bribes. The player who died makes a new character using the above rules, and gets stuck in the position that is now open.
Anything that falls into a grey area for responsibilities is handled by group consensus. If the players take to long to make a decision, I have the Commander make one on the spot (usually while somebody hums the Jeopardy theme).
All of this makes for a simple, fast campaign that focuses on the Mech action (and tanks too, but you know what i mean). There aren't any desciptions of seedy bars, I don't do impressions of maniacal geniuses, and nobody RP's character quirks. It's all just misssion briefs, game plans, and mayhem.