So, from that point of view 0VU and JW are correct.
However, as we have discussed here before, mixing on headphones is something of an acquired art. Not impossible by any means, but takes a lot of time, practice and critical self-assessment to master. There is also the issue of a significantly increased risk of long term hearing damage becaue it is so easy to crank up good headphones to serious levels and not realise it! Furthermore, headphones and loudspeakers tend to reveal different aspects of a mix, so neither one is entirely satifactory on its own.
Personally, if money is very tight, I'd probably go with the recommendation and by decent headphones to start with while saving funds for a decent monitoring system later. A cheap and nasty set of speakers and amp will just frustrate and annoy -- or it would me anyway.
As for whether to buy open or closed back, it depends on whether you intende to use them for tracking/recording acoustic instruments/voices as well as mixing. If you do, then closed back is the only way and I'd recommend the Sony 7506 or better still the 7509 without hesitation. If not, then open backed would be better, and I'd recommend the HD600 or 650.
But once again -- try before you buy because the practical and aesthetic aspects are very important to your long-term use of them.
Technical Editor, Sound On Sound