As others have said make sure you can leave no trace when cutting a plug. We cut a 3 sided square with a spade & fold back the turf, but I know you guys use a tiny knife, so what is important is not only your pin-pointing to avoid misery but you need to leave the root-ball attached so the grass grows back. I'm so careful I've dug many 1 metre x 1 metre by 1.2 metre deep holes looking for Roman remains & when it all goes back, they have no clue.
You have youth on your side, so here is what you need to do;
Be honest - No.1
Do a little more research on the house & tell them about it. This establishes your interest in History, make it very clear about how you love History.
Make sure you tell them that you are fairly new to detecting & that you don't have very many places to go.
Tell them you're a collector of your finds & you don't sell them for money.
Personally what works best for Dad & I is that we have build a huge amount of trust with all our land-owners & this can only happen 1 way. Its by promising to show them all that you find even if it were a gold coin. This WILL make you stand out from the others & it has never back-fired on us. We have people ask us to do their land now. If you want to go one step further, state that you will share some of your finds, but as your a collector you would want first pick on all finds.
Although your a collector you may find an item or a hoard which is so valuable that you would have to sell it & you would be willing to spit it 50/50.
So, if you want people to 'trust' you, you need to give them a good first impression, by doing the above.