Welcome to the Boards!
You have come to the right place for advice for sure. As for starting a tank without LR, sure you can do that as long as you have a decent wet/dry filter of some type. I have a sump w/bioballs and it has worked well for me over the years in my 55 gal tank, but others have well, other opinions on what type of wet/dry filter system to get.
A tank w/o LR is a "Fish Only" tank, a tank w/LR is a FOWLR (fish with Live Rock), so you can go either way. Do you have any plans for livestock in your tank once you get it cycled? Planning ahead is very important so that you don't end up having to upgrade things like lighting a couple of times as your desired livestock plans change-that can get expensive fast!
A couple of thoughts on your equipment, if you haven't gotten anything yet-get a decent skimmer, a refractometer, and a good test kit. These items will really help you get your tank up and running and sucessfully cycled. Oh, and one other thing-patience, patience, patience! Don't hurry the cycle, and don't add too much livestock too soon. It can take a long time to cycle and establish your SW tank and not rushing things will really pay off in the long run!
Let the questions begin!