First, don't be too upset, things like this happen to even the best of us.
Second, most people are going to tell you to not take the advice of pet store employees as many of them dont really know that much about fish.
I have the same tank you do, and I have opted to not use the filter as my tank is planted, for you, you can use the filter, but it is strong for bettas, so my advice is to baffle it at both the intake with a filter sponge, and the outflow with either a sponge or a plastic baffle made from a water bottle, you can google search instructions on how to make one fairly easily.
You have two options from there when it comes to cycling.
Cycling is important as it establishies beneficial bacteria (BB) in the filter and sponge that will eat bad things like ammonia, nitrite, and nitrates. I'm not an expert on cycling, but here is a good link you can learn a lot from http://www.bettafish.com/showthread.php?t=47838
Also, you're going to need a test kit, API makes a great liquid test that most of us here swear by.
Next, I would suggest getting a high quality food such as omega one betta buffet pellets or new life spectrum pellets, both have a high protein content which is necessary to keep these fish healthy. I would also invest in Prime water conditioner as it is very effective and a little bit goes a long way.
It sounds like you have everything else down pretty good, the heater, your supplies etc. Temp strips aren't really all that accurate, so I would just spring for a glass thermometer that hangs on the inside of your tank, they're about $3 at petsmart
Acclimating your fish: What you need to do when you get a new betta is to let his cup or back sit in the tank water for about 30 minutes, then slowly add water from your tank into his bowl/bag at 10-15 minute intervals for an hour or so (that's what I do with new fish anyway, it may be a bit over kill, but I'm super paranoid about shocking a fish)
I'm sure I left something off, but there are many more knowledgeable people around here than I that I'm sure will be happy to help you. Don't give up! These guys are very sweet rewarding little buggars once you get the hang of it. We all experience a learning curve at some point, so don't get too worked up about it :)