Since there have been many changes to the game, including solo mobs, it is easier than ever to solo.
You just have to be careful in picking your battles. Don't expect to solo a Green^^. But you should be able to solo white Heroic, or an Orange non-Heroic. Try taking on a group of 2-3 greens and see how it goes. Keep your armor at it's best so you survive longer. Use good food/drink to give you fast regen.
The higher you go, the better spells you will get. I frequently stack 5-6 DoT's on a creature plus add the pet and a few HO's. Even if the mob turns on me, I just Petrify (below level 35) and back off. The DoT's will burn it to the ground.
Conjurers have DoT's, Wizards have DD's. So use and stack your DoT's. When you get an upgrade, a new spell may use the same reuse timer as an old one. That just means it's a planned replacement and they do not stack.
Also, the higher you go, you will get spells that have additional abilities like reduce AC, slow, reduce magic resist, etc. Use those as they will help you land damage and reduce resists of your spells.
Upgrade your spells to at least Apprentice IV to get the most damage. Save the Adept I's for a few select - of if it's a loot, scribe it for free. :)
Check out
this link for a good discussion on what spells to upgrade.
You will get 3 flavors of pets, Earth, Fire, Air. The only good one is the earth pet. And when you get to level 24, you will get another earth pet. Buy an Adept III of that because you will use it for a long time. I used my level 24 pet until I was 38. I then got a Adept III pet (cost me 75g).
Don't waste time with the other pets, they are "casters" and don't last long.
Good luck!