It's a damn effective build, but I wouldn't focus on crits.
All that's important is Strength 10 & Endurance 10. Not immediately, start lower and increase with implants/OWB perks. Melee has pretty bad crits and really it's your secondary attack, plus you're gonna want to slap on as much armour as possible.
At the start of the game, dynamite will do all of the work. I wiped out all of the powder gangers in ghost town gunfight with just 2 sticks, and you end up with an unholy amount of the stuff by the time you reach Nipton. Use a baseball bat/lead pipe against critters and indoors. Wiped out Vulpes and co with two frag grenades. First Legion assassin squad with just one.
Explosives really is relentlessly powerful. By the time you reach Vegas, you're spoilt for choice. The GRA 25mm APW is brilliant, and ammo can be bought in huge amounts. For 40mm, the grenade rifle is ok start game, but I'd upgrade to the grenade launcher ASAP. You can get one right at the start of Honest Hearts. For heavy weaponry I'd go with a good old missile launcher. Missiles are pretty common at the gun runners, especially with GRA installed.
They're the three basics, outside of that just use whatever sounds fun. Mini nukes are always a blast (
), grande machinegun was spawned from hell itself, but compared to other grenade launcher isn't very economical when it comes to ammo. Red Glare is a beast, but late game, late game.
Really I didn't focus on melee at all, it was just there when I needed it. Think I was still carrying a baseball bat by the time I got to Vegas.