Titanium Mountain Bike

I would perhaps like a racing bike, but the problem is that the wheels are so small I feel like if I hit a rock I will fall, so I am like a mountain bike super light, Whats good? (Less than $ 700)

You do not fall when you ride road bikes. I have a fuji dx absolute cost me $ 500. it has the small tires (I should say something that is small, they are 27 inch tires), but looks like a mountain bike. Its 23 lbs isn't that bad. Look at some road bikes too. they are generally closer to 1k, but the weight about 18 lbs. ive hit a few bumps and huge holes on my bike and I had no problem staying on and it did not damage the bike. All good when I hit the hole that I hit I never hit it again. lol. Ive only had one person who was on a mountain bike pass me, and it was super built. He was even wearing a backpack. Otherwise I'd say a hybrid sort of. really great bike. Also look at used road bikes. My cousin just got a giant OCR1 used for $ 700. weighs less than 18kg and he said he went 63 mph down the hill on it. I think that his speedometer is broken but who knows. I hope I was helpful.

Hate to break it to you, but Titanium cost you much more than $ 700, even for the frame. Your best bet is likely an aluminum frame. You should be able to get a very solid machine in this price range.