Ableton Live is great for beginners thanks to its user-friendly GUI. Nonetheless it's also a great tool, even for pro's, although if you would like more options and to "advance" I've heard Logic for Mac is good (although it supposedly takes much longer to learn). I'd recommend starting off with Live, and from there you can pick up things much faster.
I'm not sure what trance artists use but try googling and looking around forums.
You could start using stock sounds and presets and then start tweaking them as you get more used to the interface and the buttons and knobs.
I'm also a beginner and just learning about producing. I started out with FL Studio, but found Live more easy to work with.
There are quite a lot of tutorials on Live on youtube, I especially like the one by Airbase, so if you youtube "Airbase lesson" you'll surely find something helpful.
In addition to DAWs (Digital Audio Workstation) like FL Studio, Logic, Live etc. you should get your hands on some VSTs, (Virtual Studio Technology) which are kind of like "plugins" that expand your possibilities to create sounds in a DAW, some that I'm trying out right now are reFX Nexus2, LennarDigital Sylenth1, Spectrasonics Omnisphere. Some of them have testimonials on their sites by trance artists like Above & Beyond and Store 'n Forward, so you know you can put those VSTs to good use.
Also, you should get hold on some stock sounds. I recommend the Vengeance sample packs. You can load these sounds on VSTs and tweak them.
Good luck.