I could go for the weapon I think is the coolest (which is the Perforator when combined with my 100% sneak skill and Chinese Stealth Armor, pretty much means an instant critical every time) but I don't think that counts much as my favourite, even though I use it often.
For my favourite (as in the weapon I will most commonly reach for in a tight scrape) is any version of the AER9 Laser Rifle. It's a standard weapon but it's pretty good in a lot of situations depending on which version you're using, like the Tri-Beam, Metal Blaster or Wazer Wifle. None have ever failed me and ammo is very common and easy to find, it's also a commonly looted weapon and easily repaired.
Although there are weapons that do more damage, have better accuracy or do cooler things; the AER9 is the signature, bread-and-butter weapon of the game and, in my opinion, the best weapon you can get your hands on in terms of reliability, ease of use and fantastic design.
Madnezz said:
...I've started a new game (haven't finished the storyline yet, just felt like a new game for some reason) where I chose to specialize in melee weapons. I'm trying to get the Shishkebab schematic and parts.
The hardest parts to get are the motorcycle handbrake and gas tank, the most common place to find them (and the easiest) is on the flight deck of Rivet City next to the broken motorbike. The other parts are all-too-common, you should be able to pick them up anywhere. The Schematics are easily stolen from Vance at the end of the Blood Ties questline. You can also kill Vance to obtain his fully functional but very degraded Shishkebab.
Also, if you're going for the Shishkebab it's a good idea to get the Pyromaniac Perk, which will also increase the Shishkebab's melee damage and boost fire damage from 2 to 3 damage per second for 5 seconds.
Just thought I'd offer some friendly advice there, hope this proves useful.