You will probably not be able to get a good rolling boil on a home stove for a full 5 gallon batch. Try it with water and see how it goes, you want a good aggressive boil. Also, try to cover 2 or 3 burners enough to use them, more burners are much better. If you can't get an adequate boil on your stove top do a 3 gallon boil and search for information on "late extract addition" here. It will help you get the same bitterness from the hops as the original recipe. Late extract additions will also make it easier to keep the color right because the wort is less likely to get overly caramelized.
If you already have a propane tank a turkey fryer is an excellent investment. It will properly boil a 5 gallon batch with no trouble.
A 60 minute boil evaporate about 1 gallon depending upon how aggressively you boil and the dimensions of your kettle. Be sure to take that in to consideration when you start the beer. If you start with 5 gallons in the pot you will have to add some makeup water at the end of the boil.
It is a great hobby and I'm sure you'll have lots of fun.
Once you have a decent recipe/kit the 2 most important things you can do to make good beer are proper sanitation and temperature control of your fermentation.
Clean and sanitize EVERYTHING that comes into contact with your wort after it is boiled. You should also minimize the number of things that contact your wort after it drops from boiling temperatures. I think most folks here use StarSan to sanitize and it is an excellent product. I have also used other foodsafe no rinse sanitizers with success, they are available at food service stores, but as long as you're ordering a beer kit tacking on a bottle of starsan is a good idea. For cleaning use either Powdered Brewers Wash (PBW) from the brew shop of OxyClean FREE (get the free, the other stuff has odorizers added that will not play well with beer) both are excellent and will work pretty interchangeably at the beginning homebrewing stage.
For temperature control, use the ice batch etc to cool your wort and then pitch your yeast at, or a little below, recommended fermentation temperature. Once you pitch your yeast put your fermentation vessel in a "swamp cooler"to help maintain proper fermentation temps.
As for kit preference, it is all personal choice. I love American Pale Ales and American IPAs I would try a simple Pale Ale with only 1 or maybe 2 hops. This way you will get good beer AND an opportunity to learn what a specific hops variety tastes like.