I would recommend you start with budget, powered studio monitors. Mackie, KRK Rokits, Presonous etc. And frankly if you summed the signal to mono you could get away with one monitor (for the purposes of DJing you don’t absolutely need two monitors, its just nice to have two).
Personally I’d rank the major DJ software as:
Traktor
Serato
Rekordbox
Controllers are pretty well accepted, except by the “vinyl purist” community. I played with some vinyl DJing but I’ve been all controllers and CDJs otherwise. The big thing with controllers (whether they are connected to a laptop or not) is that when you show up to a gig you and/or the sound guy have to get shit all plugged in and functioning ideally while someone else is still playing so there is no interruption in the mix. Believe it or not this can be a huge pain in the ass for all involved. With Pioneer gear all you have to do is walking with your USB stick or CDs and you are good to go.
I’d also temper your expectations a little bit. You are probably going to want to build up you skill level for at least a year before playing live in front of a crowd that isn’t just friends over for an evening. I don’t care one way or the other if people use sync (I use it depending on what I’m trying to accomplish in a mix). But learning how to blend tracks is more than just beat matching.
Whether it is fair or, yes, some people will judge you for showing up with an entry level controller and a laptop to a gig. Whoever is giving you the gig would need to know that in advance for logistical reasons (and I think that even if they don’t ask, you should tell them so it isn’t an issue at the gig).
I cut my teeth DJing gigs that were not EDM events. I played gigs were then needed a DJ to play music for 15-20 minutes between whatever was happening on stage. I played Top 40 at regular bars. I did house parties.
Yea, so your shopping list is (if using a computer to DJ):
Controller
Monitor(s)
Headphones
Interface
A couple things…if you buy a better controller you can get an interface and a controller all in one. When I recently got back into DJing after a long hiatus and wasn’t sure if I really wanted to get back into it I got a Traktor Kontrol Z1. No platters, but it is an interface and controller all in one for like $199. It only comes with Traktor LE, which is probably enough to get you started. Traktor 3 is $99.
I like this controller because it is basic–it gives you all the controls over the standard functions of a DJ mixer and pretty much nothing else. So you’d be building up you skills in a way that would transfer to virtually any other DJ system and you won’t be relying on functions you might loose when you upgrade.
There are plenty of other controllers that include an audio interface and I’d strongly suggest you look into that as you might save yourself some money.
As far as inexpensive DJ headphones there are a zillion “shoot outs” on that topic on the internet. Just pick something, frankly, if your budget is low.
As for monitors I’d defo by powered monitors and they don’t have to be studio use accurate. Again, these don’t need to be super expensive. Loud and with hyped bass is fine for DJ monitors.