It's difficult to answer because I can't see a consistent playstyle between the 40k armies. You'd have a far better approach saying what you actually want your army to do rather than try to match it with what you know. As always, the advice is to pick an army that you think is cool and then write a list to your own playstyle. Most books can offer at least a couple of different builds and so while you might want a fast hammer, for example, you'll probably find that most armies can be built to provide speed and power. Just some armies will do it better than others.
Power levels change but the 'soul' of an army tends to stay pretty consistent. Choose an army that you identify with rather than one stereotyped as powerful or providing a single game type.
If you like Wood Elves then that is a great place to start looking. I would not consider them a non-competitive army at all, and would put them firmly in the upper half of the pack at least. They simply don't play like other armies do; they will not reward you for building big blocks and slamming them about like you could for the others. They are very themed in that most options are built around shooting, skirmishing, running away and generally being difficult to pin down. Most of their armies tend to be based around cavalry and archers with negligible staying power, kiting the enemy before obliterating isolated parts of the list with Wild Rider charges.
It's a difficult army to start with because they reward control, staying at range, patience and 'playing dirty'. They will punish you hard if you allow yourself into unfavourable combats.
What kind of army did you want?
Is speed important to you? Do you want high movement, lots of infiltration, lots of flying units or the ability to ambush?
What kind of magic do you like? Do you want supportive spells to make your guys better, or hex spells to cripple the other guy? Do you like dropping magical artillery and incinerating people, or do you want to completely shut off the enemies magic through dispelling power?
Do you like shooting? Do you want artillery or massed bows/guns? Do you want to run around the enemy and pepper them, or form a line and bombard them?
Do you like to wade into the enemy and carve them apart, or to bog them down in impossible numbers?
Big monsters or big guns? Knights in shining armour, or gritty underdogs? Play honourable or play dirty?
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