all secondaries are good in pvp
some primaries are better bcoz of fast cast times
grav is a slow one
earth has - def inherent
fire is arubly the best for DoT and spiking
plant has inherent -def but is slow DoT and not really worth it
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Hi there from what you said in you post to be a good Pve and PvP solo, i would recommend either, ill/rad, ill/therm, earth/therm.
These can solo in pve very well and do great alone in pvp and in a pvp team 
I would have to say that Ill/Rad has long since been established as one of the better choices for the solo controller. My own Ill/Kin is also superb, a real Swiss army knife. But as you are new I would be tempted to go with one of the new choices Plant/Rad for instance looks great. Also given the choice between a controller or a defender I would go with the controller.
@Boy Wonder
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Leader of the Legion of Heroes
agreeing that Ill/rad is a brilliant solo troller. It was my first serious character and although i don't play him too much these days, he is still an absolute blast whenever i do. radiation is still my favourite controller secondary (and probably my favourite defender primary too) it just is able to debuff everything whilst buffing quite a bit too. Illusion differs from most of the other control sets as it possibly lacks the hard control of other sets. But this is set off by having rather high damage potential. Key powers are Spectral wounds (a psychic blast essentially), blind (a single target hold), superior invisibility, Phantom army (get this at 18 and love it, it summons 3 indestructible decoys who last for 45 (iirc, its been a while!) and generally annoy the enemy and have a built in taunt effect so that they get it not you.), spectral terror (an unkillable stationary fear causing pet) and finally your Phantasm (a permanent but killable personal flying energy blaster, complete with his own decoy!).
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[ QUOTE ]
all secondaries are good in pvp
some primaries are better bcoz of fast cast times
grav is a slow one
earth has - def inherent
fire is arubly the best for DoT and spiking
plant has inherent -def but is slow DoT and not really worth it
[/ QUOTE ]
Er? Grav a slow one?
Perhaps you should consider Propel, giving Grav the highest ST damage output of any controller (pets aside, but I having tried every controller pet I find Singularity the best of the bunch)
Solo, my gravity controller solo'd fastest. In fact, ill give order of my controllers (all played to level 38) in terms of soloability:
Grav / Rad first
Fire / Storm second
Earth / Sonic third
Ill / FF last
(I have played plant and ice dominators to level 50 and 41 respectively)
My order of pet superdupeness:
Singularity, Jack o Frost, Stoney, Imps, Phantasm, Venus Flycack (awful)
(PvP is a different matter of course, but again, the high spike damage of a Propel on a contained foe is the highest spike you will get as a controller primary)
Firstly I'll say that I don't PVP and personally I don't think that the game is really designed for it, it's been tacked on and powers adapted to allow for it. If pvp is what you're really after I would suggest that you look elsewhere.
If you are serious about pvp in CoX then certain Blasters on the Hero side and Doms on the villain side seem to be the way to go.
If you want to use a Controller then Ice/Rad seems one of the better ones due to all the slows, Mind/Rad should also be good due to it's ability to stack different types of Mez.
Others with more experience in this area will I'm sure supply other builds.
On the pve side it really depends what you mean by good soloing; for me soloing means doing missions and being able to handle what ever comes your way, to others mean street sweeping so that they can level at the fastest rate.
If it's doing missions (you will still level quickly)then IMO the winner hands down is Illusion, pair that with Rad, Storm or Kin (others will work but in my opinion those are the best (i'm sure TA will come up but I've not tried it)).
With either of the above combos you will be able to solo pretty much anything, the only thing I've not tried are AV's and GM's, although others have with these combos.
For street sweeping IMO the winner is Fire with rad as the secondary. You basically jump into a mob using hotfeet to deal damage and cages to setup containment; rad is useful for the -tohit in IR.
Other secondaries that work well are storm and kin but rad will IMO be the smoothest ride from 1 to 50.
Mind/kin would also work although it will bloom late on when you can use the Mass Hypnosis - Fulcrum Shift - Terrify combo.
As Cognito said Grav/Rad is a decent combo, again you really need the -tohit of RI to reduce the damage from the mobs while you spam Crushing Field and use Propel on the Bosses; I found Dimesion Shift useful for splitting large mobs while doing this.
So in summary Illusion /Rad, Storm or Kin for missions, EB's etc
Fire /Rad, Storm or Kin for street sweeping and fastest leveling.
Then Mind/Kin followed by various other combos.
Earth and Ice the worst for soloing.
All of the above is just my opinion, but it is based on years of play most of which was with Controllers.
L50s: Tanks: Cryofission - Ice/EM - Dr Celsius - Fire/Ice - Saint George - SD/SS | Controllers: Psichosis - Ill/Kin - Major Chaos - Ill/Stm | Scrappers - Neutron Crusader - DM/SR
Currently Levelling: Angelic Blade - BS/WP Scrapper | Seeds of Destruction - Plant/Kin Controller
Although you talk about wanting to solo initially, I do detect that you want to team when you feel ready. I've no doubt that for pure solo ill/Rad is a winner however for the most fun from 1 to 50 solo AND in teams I'd suggest fire/rad, is an excellent 'all rounder' in PvE and will hold it's own in the two lower level pvp zones. From my limited experience the two higher level PvP zones belong to those folk who want 'pure' PvP builds.
Fire/Rad holds it's own challenges however in endurance management mostly
Earth/Storm king of PvE, hands down. Guffy knows it.
@False Fiction - Virtue / Defiant
Current projects - [Glaciologist - Ill/Cold Troller] [Cloudshaper - Storm/Dark Def] [Harald Wartooth - Elec/Psi Domi]
go ill/rad or ill/storm if your feeling adventurous
Controllers
for pvp : ill/rad, it's in the upper 10% of all pvp AT's. Also not shoddy for pve.
for pve : fire/kin, boringly enough.
Defenders
for pvp : rad/psi
for pve : anything 
.. but kin/elec is amazing in a team and an empath is always wanted sub lvl 35 or so.
Beware though, for serious pvp you need purples and LOTG 7.5%'s. Set aside ~billion inf for a full build at 50.
Discalimer : Above is my opinion, garnered from faceplanting too many times
Fahie
ps. Obviously I'm biased on the troller sets given my signature but they are honestly both *that* good in their fields.
Hi there!
. Now I didn't say the BEST at soloing PvE and PvP, but capable, not so hard that it stops being fun! Obviously I still want to be good in team play, and I'm sure any defender/controller is. I'm aware this is solely Controller forum, but perhaps what I really want is defender and I'm sure guys can point me in the right direction if I'm in the wrong one now!
I've read all the guides I can find like ENANTIODROMOS' GUIDE, etc,
And am still pretty clueless, I played this game about 2 years ago, and am now returning to it, since it's arguably the best MMO for people who don't have a lack of life to grind 24/7 and "be the best"
Also I'm a super hero nerd ^^
In any case I want my first "real" char to be a controller/defender, something more interesting and
"harder" (in my mind) then the "dps" scrapper and blaster, and tank.
My main priorities for first char are soloing PvE, PvP, since it's a first toon I don't expect to find the greatest team instantly
I had a grav/kin controller last time I played, not high level, but I still felt that in PvP I'd be limited.
Obviously I know there is no toon great at Everything, but if you just give me options and tell me the pros and cons it would help me immensely to choose who I shall be!
Any help is much appreciated