Where 2 plant young peach tree

New to the gardening game having just moved house, mainly to gain some outside space my neighbour has given me a peach tree. Its been grown from a cutting and still in a pot but obviously needs planting out. Could I plant it in the lawn, (just seeded in the autumn, one of my first jobs since moving in), or I've read somewhere that you can plant them by a fence and train them up the fence.
This is my first of many queries, I'm looking to gain from eveyone elses experience!!!