This game is not like CoD in that you are always limited to the first five starting weapons (Lancer, Retro Lancer, Sawed-Off, Gnasher, Hammerburst). From the multiplayer options menu, you can rotate your primary and secondary weapons between these. However, you will never be able to start with weapons other than these.
During multiplayer matches, one useful strategy is to learn where better weapons are in each map and try to get them (e.g., if you like using the Longshot, know where it is on each map).
You also mentioned that you have to shoot a lot to kill but go down easily. This may be due to a few factors. One is that they may have better accuracy then you and are getting headshots. This game has been out since September, so don't be suprised that people are ridiculously accurate. Another issue is the perfect active reload. Your opponents may be emptying clips at the beginning of the match to get to perfect active reload for quicker kills. To perfect active reload, while reloading, press the right bumper button while the moving line is within the white line. This will have varying affects on your weapons (e.i., some will gain damage, lose spread, or increase fire rate). This is a necessary skill in order to survive in multiplayer.