I tried to research these questions, although I have never acted upon it and put anything in the ground, for a variety of reasons. Probably you can get definitive answers if you read one of the sources I quote below.

You need two trees for cross-pollination (I have read "different varieties", but usually cross-pollination means two plants grown from different seeds, and since it is always seed grown, never grafted, any two plants probably suffice, though I can't be absolutely sure about that). They need considerable shade for the first year in the ground, though later they need good sun (reflecting their forest origin), so it is traditional to put them in a sunny spot with a bottomless barrel around the young plant for the first year to shade it, or else growing up in the shade of a fence that they will emerge from. They need to be put in the ground as soon as possible, they don't like being pot-grown for an extended period and then put in the ground. I have seen "5-10 years for first fruit" quoted.

The only supplier I have discovered who can give you a named variety (as a plant) is www.agroforestry.co.uk (plants sold out for this season). In the past they had more than one plant variety on their list, but now I only see one, so to be safe you may need to source a second plant from someone else. They also sell seeds: the instructions are "cold stratify 13 weeks" so you may be a bit late for this season to do that (if seeds with such instructions are within your capability, I've never succeeded).

They also sell these publications:

Factsheet F08: Pawpaw - Asimina triloba Price: £1.50

Uncommon Fruits for Every Garden
by Lee Reich
Timber Press, 2004. ISBN 0-88192-623-X. 288 pp. £17.99.
This fine book is a collection of over 20 monographs on unusual fruits, most of which are uncommon in Britain and the information about them is of great value to anyone thinking of growing them here. They include juneberries (Amelanchier), beach plum (Prunus maritima), musk strawberries (Fragaria moschata), pawpaw (Asimina triloba), raisin tree (Hovenia dulcis), lingonberry (Arctostaphylos uva-ursi), hardy kiwi (Actinidia), mulberries (Morus), persimmons (Diospyros), Elaeagnus, maypop (Passiflora incarnata), che (Cudrania), Nanking cherry (Prunus tomentosa), Lowbush blueberries (Vaccinium), jujube (Ziziphus) and the shipova (xSorbopyrus).

Agroforestry News Vol 2 No 2
Gaultherias, Hazel (1), Pawpaw, Beech, Ground covers (1), Grafting - rootstocks. Price: £4.00

Agroforestry News Vol 9 No 4
Forest gardening: Plants for difficult sites (3) – small shrubs, Hicans, Ink disease, Peaches (2), Plants for façade insulation, The soil foodweb, Asimina triloba – pawpaw. Price: £4.00