Should my primary focus in aikido be keeping myself off the ground, or taking my opponent down? And with both ways, what are some good strategies?

Keeping yourself ON the ground!!!
So long as your on the ground, its sorta easy to manipulate your opponent.

Often times, I have jumped, so as to tackle an opponent. It sometimes works...... What do you think?

The main rule of thumb in Aikido is to ALWAYS keep both feet on the ground. Yes, there may be certain situations which call for taking one foot off, but if those situations are not present and you are floating in mid-air, you're opponent is likely to lift you out of the ring with ease.

Thanks. I recieved training from Morbon. =)

You can also check this: http://forum.toribash.com/showthread.php?t=137626

Their advice about keeping the feet on the ground is correct for the most part, but don't neglect the opportunities that require your feet to move off the ground. I have won many games where I took the opportunity and jumped to dq them or force them out of the ring.

If you jump there is lotsa force you can use to manipulate your oponent so losing ground is not bad at all if you are able to handle it.
it is more fun too ^^

if you get lifted try to get over you oppenent so he can not push you out of the dojo or try to reach the ground. raising arms, what beginners very often do, is the worst idea.

if you are still a beginner you should try to learn the basics first though.

i usually tend to keep both feet on the ground for as long as possible, or untill i come into a good position to make a throw or takedown. and always try to throw them off balance, when people do kicks is when its the easiest.

I like to keep one foot on the ground , and one leg contracted. So when I', falling I extnd me knee to save myself and regain balance.