morrisons i can comment on, i dont use asda.
moving from macro beers such as bud etc. you dont want too much of a shock to the taste buds.
moorlands Old golden hen. cracking easy pint with good hop flavour, not strong on bitterness but with a good flavor profile, excellent transition ale.
boston lager. ive seen it get a bad rap but honestly its a good lager for someone un familiar with craft ale, try it.
greene king ipa export, good beer with a bit more bitterness and slight hoppy flavor. definitely a good transition ale.
my three for you. you dont want a massive hoppy beer to start with, sierra nevada a must when you get accustomed, goose island or a good pint of guinness will do but start small. you will grow to appreciate.
must get to a m&s jester and give that a go.