FL studio, reaper, reason, and renoise are good places to start. reason and renoise aren't recommended if you ever plan to do live recording though, they're more for people who work all in the box. reason is the most expensive of those but also comes with the most ready to use stuff, if you use FL/renoise/reaper you'll probably spend a lot of time finding samples and synthesizer patches and such where reason is very useable out of the box in that regard. FL also comes with some decent stuff but also some bad stuff.
reaper is...actually fully functional in its free version, it just uses the honor code basically that if you profit on your music you're supposed to buy the license -_- renoise is the next cheapest, IIRC like 75 euros, it has a very unconventional interface though that you will either love or hate...FL goes for $150 for the fully featured version, it's pretty newbie friendly. reason is the most expensive one I'm recommending at $500 but as I said before, comes with the most useable stuff out of the box.
note that none of these programs use staff notation with the possible exception of reaper(haven't used it much, heard excellent things about it though). FL, reason, and reaper use something called a piano roll where you draw notes on a graph where Y axis represents pitch(a piano graphic is shown on the left) and X represents time(bars and beats are displayed horizontally). renoise uses a totally different approach where time is vertical and you type notes and articulations in...in any case, downloading the demos for these would give you a better idea, as I said, reaper's free version is fully functional and FL and renoises are pretty useable too(renoise demo can save songs but can't export to wave, FL is opposite and can export audio but can't save project files)