You'll need 20 for the guy lines and poles alone. Add another 10 for any interior fixings and I think you'll be safe. You can always pick up some more if you are a short.
You may need a range of peg types depending on the pitch type and what you are pegging!
Personally I have abandoned the cheap useless pin pegs which are always supplied with a tent. I am probably overdoing it but I now take 3 types: channel pegs for the corner D rings, ground anchors for the guy lines and rock pegs for the ring & pins. I take enough rock pegs for all pegging points in case the ground is too hard for the other peg types.
Lots haha - we always make sure we have a lot more than the pegging points as you quite often need them (we have just the cheap pegs as cant afford the other ones) weve never had a problem with them though to be honest, don't find they come out or anything etc. We do use some of the flat top heavy duty ones for each corner of the ground sheet. The rest are cheapies.
------------- June 2015: seaview international 2 nights
July 2015: little winnick 2 nights
August 2015: lower polladras 5 nights
august 2015: tollgate farm 5 nights
august 2015: oakdown 3 nights
September 2015: tregarton park
family of 6 with young children
Sorry, I can't remember how many we used but I do know we always had a selection of different types. I hope you enjoy the 'Eagle', we still have ours in the loft as we now have a static. We only used the tent for 5 nights as we got flooded out so bought a tourer & had it on a seasonal site but have now gone to a static. What we did find though was the footprint and carpet made a big difference.