Great ways to build experience are easier to find than you may think. Using Fury against large groups of enemies is the most effective way I have found to build up quickly. If you use it against the two thugs that appear around the hotel guarding the enterance of the hotel for the mission to acquire the bank truck.
Also a great technique is to break (condition 0%) a pair of very low level brass knuckles and then use them to punch a fallen lone zombie in the arm. (knuckles use the least stamina and the broken weapon is less powerful than fist alone) Often it takes two punch combos to break (break being a condition that leaves the arm useless and awards the user 1/4 of the enemies experience) his arm repeatedly, but sometimes aiming at or slightly below the hand will allow you to break with every punch. Do not run out your stamina or the zombie will start moving. A great way to use that technique for the full effect is to run into a thug with a truck causing him to fall, and then attacking him with the broken knuckles. Often if performed correctly this technique can earn you 3 to 10 times the experience of the enemy's death.
In the beginning when your level is low (under 10) your weapons are not going to be useful for long to it is smart to not upgrade them unless you get an orange weapon. It is best to use them and abuse them. Then sell them to make a good foot hold for starting out the game with some cash. After building up to level 10 or so it is best to start collecting, once you get to level 20 or around act 2, it is best to have fully upgraded weapons.
Based on the situation you should learn which weapons you can use the best, I find that having a very powerful one handed weapon is a life saver against multiple infected running at you. When fighting a thug a good two hander with a longer range makes it much easier to dodge. Rams are very similar to thugs dodge the charge and then hit them with a two hander.
All mods are a double edged sword always remember that, when hitting a zombie with a critical hit they will sometimes take series of additional damage from the element of the modification. ( if you get to close so will you) But the best thing mods do is critical hits, making your enemy cease attacking and becoming vulnerable, especially bosses. But in rare occasions that may make things more difficult. (specifically in situations where you are surrounded or are in close quarters) So sometimes it maybe better to trade the modified weapon for a plainer weapon.
An easy way to defeat the Infected is to hit them with a flame weapon.
An easy way to escape or fend off 2 or 3 zombies, if you are cornered, is to press jump then kick in rapid succession. If timed right you have a high chance of doing serious damage as well as knocking over walkers and infected. This is an effective method of stopping infected in their tracks. Infected and Walkers will always be knocked down by the attack, allowing the player a golden opportunity to kill them before they get up again. As in a situation where you're surrounded, the jump kick wil knock over several zombies if done right, giving you that perfect opportunity to escape if need be.