You do need a mixer of some sort. The VocoPro mixer is not great. You can get a true mixing board for about the same price. There is a key changer on the player so the mixer does not need this part - which is typically what make a 'karaoke' mixer is the addition of a key changer.
For the same price or close to it, take a look at:
http://pro-audio.musiciansfriend.com/pr ... sku=630156 - only two mic channels but much better sound & versatility over the VP.
http://pro-audio.musiciansfriend.com/pr ... ku=630139V - even comes with a couple mic channels with compression - nice for karaoke.
http://pro-audio.musiciansfriend.com/pr ... sku=630166 - if you need a couple more mic channels
Now all of these will blow the VP mixer away, all have built in digital effects over the basic built in echo of the VP.
The PR15 are not a powered speaker, the other ones are, you will need some kind of powered speaker OR a separate amp with the Peavey PR15. But powered speakers will eat into your budget quite a bit as even cheap ones run about $300 a piece or better. These run about $280 a piece.
http://pro-audio.musiciansfriend.com/pr ... sku=600735