weeds in new lawn

I have a new lawn that was seeded last october (by the builders in my new house ! )it has not had one cut yet. The problem is it is full of weeds (all types). When is it possible to first of all give it its first cut and also apply weed killer

 

I'd give it a cut now - it must be getting a bit long?
Weedkiller I'm not sure, but other seem to be doing that now too.

 

keep it cut short or the weeds will set seed and you will have even more weeds