The good news is that there is no best class or race. There may be initial differences in stats, but over time you will get gear and items that will boost your stats beyond whatever initial gain you had.
If you are a Necro, you will primarily want gear that boosts your INT.
There is an abundance of solo mobs throughout all zones so you will have no problem soloing. Bad news is that solo mobs will only give you solo loot. Group and heroic mobs will give much better loot. With standard equipment and spells, you will only be able to take on a heroic mob that is several levels lower than yourself.
Here is a complete spell list for Necro's.