We're FTB too. I really recommend the Phil and Kirstie book How to Buy a House for advice on hearing about properties first and being attractive buyers.
I think two things that have helped with our purchase (complete in 2 days!) is
A) we were on the estate agents books of potential buyers so heard about the house before anyone else.
B) we sold ourselves to the estate agent - already have a mortgage broker and established how much we could borrow, lovely couple and little child looking for our family home, renting and can move at v short notice, not fussy about dates, etc.
And we were quick. Told about it on Tuesday. Viewed it Wednesday (it was obvious from the agent he wanted us to see it - liked us as potential buyers, see point B), offered the asking price first thing Thursday, accepted on Friday morning.
We later found out we were not the only offer but the vendor liked us - we took our DC with us and complimented them on their home and thanked them for letting us have a look at it.
Maybe none of that was what helped but I think it did.
Also hang out with us on the Buyers Support Thread. Even if things are going ok it's great to have company.