Well, the choices for you then would be:
Thermal Radiation
Kinetics
Radiation Emission
Dark Miasma
Storm Summoning
Right, let's have a look at these see how they match up to your needs;
Thermal Radiation:
Can it solo? Yes. However, it's soloing tools are only available much later on. Up until 35, you only have 1 power that you can use on yourself, your AoE heal.
Is it teams friendly? Very. As mentioned, most of the powers in the set are team based - you have a single target heal, 2 resistance shields, a resurrect, a mez protection power and a +accuracy +damage power. You also get some great debuffs. Teams will love you.
Summary - the best "healing set" (some people hate the term healer in this game, myself included. Buffs & Debuffs are far, far more useful) on villains along with some decent debuffs and great buffs. However, you will likely feel like a buffbot/healbot at times and soloing will be a little difficult before 35. You'll spend a few seconds every four minutes re-applying your 2 shields and using Forge (+accuaracy +damage ally buff) when it recharges.
Kinetics:
Can it solo? Yes. With 2 +damage powers, a great heal, an endurance drain/recovery power, 2 built-in travel powers and a +recharge power, it's a great set to solo with and a very popular secondary for farmers. However, some people can find it a little lacking until lvl 38.
Is it team friendly? Very. Those 2 +damage powers also affect your team, as do the heal and endurance powers. You also have a decent mez protection power and +recharge & +recovery power. Teams will like you before 38, then adore you afterwards.
Summary - one of my favourite sets, it has the 2nd best AoE heal in the game, but it requires a tohit check so it will miss occassionally. Some people dislike Speed Boost (the +recharge & +recovery buff power) as it also increases their run speed to Super Speed levels. Soloing pre-38 can be a pain for some people. You'll spend a few seconds every 2 minutes re-applying Speed Boost.
Radiation Emission:
Can it solo? Yes. Probably the best of the bunch for solo play, the two debuff toggles you get (-accuracy & -defense and -damage & -resistance) will make life easier, safer and faster. With a few other tools, including a +damage, +recharge & +recovery PBAoE buff and an AoE heal, soloing should be a breeze, even if it does take a little more thought and endurance management.
Is it team friendly? Very. Whether it's to debuff an AV into the ground or just mince though masses of minions, Radiation Emission has the tols for the job. Throw in the 2nd best ally resurrect power in the game, a power that debuffs enemies around a dead teammate, a PBAoE hold toggle and a PBAoE hold attack (sans the damage), there's soem great tools. Teams will worship you.
Summary - probably your best choice, as it doesn't have any single target ally buffs, so you don't have to worry about being a buffbot. It's great solo and in teams so you get the best of both teams. However, the AoE heal is a little lacking, although you'll come to realise that, with everything Radiation Emisison has to offer, you'll forget you ever needed to heal.
Dark Miasma:
Never tried it myself, so I'll just put out what I know - it has the best AoE heal in the game, although it requires a tohit check like the one in Kineteics. It also has the best ally resurrect in the game - it's AoE! Fear is handy and there's a little of that in here.
Storm Summoning:
Again, not a set I've played myself but here's what I know. The single target heal isn't great, but it does recharge rather quickly and has some nice mez proetection built-in. There are a few pseudo-pets which lead to a lot of control and damage mitigation.
Hope that helps, my eyes hurt now