some of my sweetcorn varieties were iffy to germinate indoors. As for aubergines outdoors this early..well that's optimism
. Mine have been out for a couple fo weeks and moved to the cold glasshouse and not grown a heap even there. Melons will germinate quite well indoors like most squashes.. by courgettes are big enough that they need potting on from 3in pots. 2 will go in the greenhouse border for an early crop.. then get ripped out when the field one's start.
B&M stuff not usually a problem.. although i check against wilko's and see what the poundshop and ebay have...'cos I'm mean. You can just buy a melon and sow the seeds from that too - wonlt be the fancier colder climate stuff but in a good year you may get lucky.
If you
really want to get keen...then sow some lemon pips, date stones, lychee stone etc.. most of them germinate well in the airing cupboard - it's just the greenhouses and heating afterwards!! Oh and a piece of ginger root will grow too...lovely flowers if you get it that big.