Take it from a beta tester, take a slotted passive defensive power as soon as you can, it'll make soloing a lot easier. Invulnerability from the Power Armor set, Defiance from the Might set, Personal Force Field from the Force set, Regeneration from the Supernatural set. It will make your life a hell of a lot easier since these powers either make you heal faster, or boost your defense. Also available are slotted passive offensive powers, these aren't quite as good as the slotted defensives for soloing, but they also make fighting a lot easier by adding to your damage, or helping you regenerate energy. These aren't required to get along by any means, and if you've got a group then you'll likely not need them (unless you're playing a specific role in the group) but they help a lot.
Also, if you're using a hero who's basing powers around strength (Martial arts, Might, Power Armor, etc.) then remember that you can pick up cars, and later armored cars and larger items. These are extremely damaging to many enemies and are great against fliers if you're a melee hero.
Edit: A few of mine, most are much lower res because they're saved directly from the costume creator.