Matt Baker's father was also a military man just like him, his parents divorced when Matt was young. You can see from the flashback's of Matt's home that his family was not poor. When his father was leaving, he decided he'd give Matt the pistol as a means to remember his father since he'd not be available always to visit Matt since he was a military man and had to attend to his postings, etc.
Matt rejects the pistol since his mother doesn't want it in the house, and also because his mother doesn't want him to become a soldier like his father.
His father died during service (it is not mentioned exactly when, but it is assumed between 1931 and 1939), holding this pistol. Sergeant Hassay ("Mac" in the game) retrieves the pistol and it is given to Matt at the funeral to keep. Since then Matt has kept the pistol with him as a memory of his father.
The deal with the pistol is that in the first two games (and even this one), anyone who holds, uses, or plays with the pistol other than Baker himself gets killed. A small part of the story revolves around this fact, causing Baker to think the pistol is cursed.
As for the spectacled guy (Legget), he is dead by the time of Hell's highway though Baker still has hallucinations of him, he also died holding the pistol, and what he did will be shown later on in the game, it was a big secret even in the past two games
I did not cared much about the plot when I played this one - every WWII based games have good historical ( sometime imaginary though ) plots - the only thing that matters for me in such games are gameplay, controls and action - I've not completed the previous two BiA titles but this one is the best WWII game to me - other good WWII games are CoD2 , CoD Waw, MoH Allied Assualt, Breakthrough, Spearhead and MoH Airborne
The Brothers In Arms series has the best plot of any WWII game, hands down. The situations and desperation you find yourself in seems very real at times. At the end, I found myself caring a lot for the ultimate fate of my squadmates.
It was disheartening to see what happened to a few of them though. I hope to see more BIA games, this series is one of the shining examples of great story driven games.