Hardware mixer - One got 2 channels for incoming signals and the other have 4.

You either can use 2 channels for the software or all 4,or use 2 for the virtualdj and the other 2 for external sources like cd players in case your software crash.
Software - Using the MC3000 as an example - It's a 2 channel controller BUT you can play with 4 DECKS in the software by flipping through the decks using the same 2 channels.
Channel is Deck A/C and channel 2 is Deck B/D.For most people 4 channels is a waste,unless you want to use it for backup.
With time code you control the software with cd's or vinyls which contain the tone signal.However,timecode has limited use.When using timecode on cd you can't use your cdjs built-in effects,auto beat loop and master tempo.You'll have to use these in the software.VDJ's timecode is free on the website if you use cd players.If you use turntables you need to buy the time code vinyls.With timecode you can't control video,well you actually can but you need an expensive midi mixer to move the crossfader.
Maya44 is perfect.It was so popular that they brought it back after it was discontinued.If you have cd players and mixer all you need is the laptop.Since you are looking into budget friendly options,rather go for the mixtrack pro.
edit:nice thread by the way