What's a fast way to get built up in Black Ops multiplayer?

Well, before I jump directly into answering this, lets investigate the ways you can gain the most money, which in turn allows you to buy the most stuff.

Contracts

Its partially depends on your ability to fulfill contracts. If you can successfully complete high reward contracts you will gain more money and more experience at a greater rate then players who cannot. Try and make sure you always have an 'active' contract so your kills are constantly working towards something.

Gun Challenges

Its also worth noting that more kills trumps completing challenges almost every time. What I mean by this is don't spend your time on a gun you suck with for experience. The opportunity cost of the kills you didn't get by using a crappy gun greatly outweighs the experience you gain from the challenges. By using a better gun you'll get more kill streaks which in turn gives you more experience and more kill streaks, and kill streaks also give experience!

Kill Streaks

Pick low kill streak rewards (as these provide you with extra experience every time you call them in) and try and get these often (hardline?). Keep in mind that getting dogs, while awesome (11 kill streak) provides THE SAME AMOUNT of experience as calling in a spy plane. By using low achievable kill streaks you will gain more experience by using the kill streak, gain more experience by challenges for the kill streak, and gain more experience by the kills you get when your kill streaks are up! Most of this game is about snowballing your momentum.

Equipment

One of the most often over looked ways of gaining experience. Not utilizing your equipment is bottom line a wasted opportunity. Don't think of throwing that flash bang grenade as -wasted- think of it as utilized. Every time you die with out throwing your flashbang you have wasted the opportunity to potentially save your life, potentially get a kill, and work on your equipment challenges. Wasted equipment is sad equipment. Utilized equipment is just one more lair of the snowball (see above)

Keeping these things in mind will help you level up faster, but its worth reiterating the most important part of this description. If you are using crappy perks and crappy guns to get challenges YOU WILL LOSE EXPERIENCE. The smarter you play (low kill streaks, great perks, great gun) the more kills you'll get which will lead to more kill streaks which will lead to more challenges which will lead to more experience!

Thesis

Now this seemed like a long detour to the point, but here it is. If you play better you can afford to buy more points. There is nothing wrong with "This looks neat" when you have a ton of cash laying around from following my above examples.

As far as an 'optimum route' this really depends on how you play. Ever had a friend argue with you for hours about how 'their xyz' is always the best but it just doesn't work for you? You and I will be significantly better with different guns and different perks, but you wont find whats 'optimized' for you until you try it. Buy as much as you can and try it out on a 'test' class while you get a feel for which guns and perk choices fit your play style best. Want a pink rabbit emblem on your Famas that is strictly asthetic? Go for it. Want to try a new gun? Go for it. Just make sure you always dedicate a class to something you know you can kick ass with. That will give you a fall back while you investigate which perks and guns are good for you!

Hope this helps

Starting Classes that work for me

While purely subjective, here are some classes that might help you get started

My favorite assult rifle class (5 k/d ratio) large maps

• Galil (best assult rifle I have unlocked so far could also be Famas)
• Red dot + Silencer (keeps me off the radar)
• Frag + Concussive grenade + claymore
• Hardline or Ghost (depends on amount of spy planes)
• Warlord (for the 2 attachments)
• Ninja (if you wear a good pair of headphones it will change your life)

My favorite SMG class (4.2 k/d) Small maps (NukeTown etc)

• Ak 74u w/ grip or silencer
• Semtex or frag, concussive, and Motion Sensor
• lightweight or hardline or ghost (depending on map size + spy plane)
• hardened (Bullet penetration, may have botched the name)
• Ninja (as always)

Edit: Found this for another question, thought it would be applicable here as well:

Call of Duty Black Ops Weapon chart with damage, range, rate of fire, recoil, ammo, reload time, and body multipliers to help you choose the right weapon for you =)

Another good source of credits/XP is the headquarters game type. You receive +50 score every few seconds. This is a good list for ways to level in Black Ops (though, Aardvark did an admirable job of covering most of them).

Another suggestion would be to equip ghost as your tier 1 perk, sleight of hand as your tier 2 perk and a Strela-3 launcher (similar to the Stinger in Modern Warfare 2) to take out enemy air support.

You gain a lot of XP from shooting down helicopters. Plus one of the ghost perk pro challenges is to take out 30 enemy air support without a killstreak launcher (SAM turret/Grim Reaper)