Levelling a bumpy and scruffy lawn

I am putting a new patio in and would like to use the opportunity to also make my lawn nicer.  I'd like a lush, green lawn, not the bumpy scraggly one I have now.

Should I:

1. Remove the existing lawn, scrape off an inch of soil, rotavate, add top soil and new turf.
2. or...  Just get a ton of top soil and rake it nice and flat over the top.  Then seed.
3. or...  Kill the old lawn with weedkiller and rake new top soil over the top. Then seed.

Obviously, options 2 and 3 are cheaper than removing and digging the old lawn.  But would they provide a decent lawn?  What should I do?

Pic of my current lawn is below:

 Thanks!