Couple of points to add (purely from my own personal experience, as always with fish your milage may vary).
If you add water straight to the tank (ie with a python type system) make sure you match the temperature of the water. My DIY python system attachs to both the cold and hot taps and I run the water out of the drainage tube to check the temp before putting it into the tank. a python water changer (or DIY version which is easy to make) makes water changes a LOT easier.
Also if you add water straght into the tank make sure you add the chlorine remover as you go and give it some time to take effect before turning your filter back on (oh yeah, make sure you turn your filter off first!).
Dont add to many fish at once and make sure your tank is cycled first (search for "fishless cycling"). Take your time and monitor the ammonia, nitrite and nitrate or you could end up killing all your fish.
In general if one fish can fit another fish in its mouth it WILL eat it. Also if a fish has long whiskers this usally means it is a predetor and will actively hunt other fish.
Make sure you keep doing partial water changes. 50% water changes are perfectly fine as long as the PH/KH of the tank water is similar to the PH/KH of your tap water. Unless you are using CO2, PH buffers or water softening methods then there is not going to be much difference between your tap water and tank water (except for the stuff you want to remove from the tank).
Do get to know the people at your LFS and check out all the LFS in your area. In my experience the guys at a good LFS are a fountain of knowledge. You can normally tell a poor LFS by the quality of the fish and the tanks they are kept in. Ask what they feed their fish on, how long they keep them for before they are sold, etc, etc. As said before if one person there doesnt know everything this is not a bad thing, they could be new to the job and as long as someone there is willing to answer you and knows what they are talking about you will be ok.
Get at least a Ammonia, Nitrite and nitrate test kit. Test your water a lot when you are cycling and for the first few months after you add your fish. If you notice any spikes do more frequent water changes, check how much your feeding and other factors that can cause spikes in the water chemistry. After awhile you will get to notice by the fish behaviour if there are any changes in the water and only need to check if you notice anything wrong (sharp increase in algae, fish losing colour, etc).
PH and KH test kits are good to get a base line of your water but unless you use CO2 or PH changing substrates/buffers your PH shouldnt change to much. Regular water changes will keep the tank water PH/KH close to the tapwater PH/KH
Feed a varity of food to your fish, not just flake food, this will help keep them in good condition.
In general if a fish is supposed to be kept as part of a shoal you need at least 6. More is better if you have the space for them. There are exceptions to this but for the likes of tetra's, danios and barbs this normally holds true. If you dont have a big enough shoal they will not feel comfortable and may hide away.
Some good first fish (cheap, hardy but pretty and interesting fish):
Glowlight tetra's - Never normally look like much in stores but when they get settled in to a tank and are well cared for they get a very bright red colouring and are very pretty. The are active in the bottom-middle area of the tank and like to shoal together (they will also shoal with other tetras).
Tiger Barbs - Important! These can be mean little gits. Do not keep with long finned fish, ever! You also need to keep a fairly large group of them as they will fight amongst themselves and in a smaller group you might get 1 or 2 being picked off. If you are keeping them by themselves or with other hardy fish they are fairly interesting fish and can survive changes in water chemistry that will kill other fish. You can also get in a number of colour forms. Just remeber they are aggressive. They tend to stay in the middle-upper area of the tank.
Cory's - Very cute cat fish. Make sure you get at least 4-5. They dont get too large but you still need a fairly large tank to get a decent group in. Again very hardy fish that are available in a varity of colour forms. Make sure that if you do get a group they are all the same type (different colour forms will most likely not shoal together).
Zebra Danios - Very active blue and yellow fish. Available in a couple of colour morphs and also in a long finned varity (which is my favorite). They tend to stay in the upper 1/4 of the tank so make a good tank mate to a shoal of Tetra's that tend to stay inthe lower level.
Silver tip tetras - I only saw these "in the flesh2 at the weekend and they are quite stunning (much nicer then any photo I have seen). Like most tetras they need to be in a group and will stay in the lower part of the tank for the most part. They have a golden coloured body with silver tips on there fins. Against a dark background and in a planted tank it looks like they hive little lights on the tips of their fins. I was so impressed I have decided to get these for my new planted community tank when it is cycled.
Gupies/Mollies/platys - To be honest I have never kept them but they are all fairly easy to keep and will breed with little effort (especially guppies!).