If I play this without playing the previous Fallout titles, will I be lost?

I don't think it's designed that way...

Worst case, read the Wiki.

no, you will only miss 2 games that are probably far superior than Fallout 3. Fallout 3 is like an unwanted child bastard of Oblivion and Fallout.

No you won't and disregard Shios comments, hes quite negative.

^So the originals are better?

It depends if you're into retro games or not. The pacing and game play might not be what you're used to.

Are Wasteland and FO 1 and 2 like THES: Arena and/or Daggerfall? I ask due to its free roam ability and sandbox nature.

 Exactly. Fallout 1/2 are great games for their times, but you may not find them easy to play at all.

All 3 take place in the same world, but from what I've read, you need no prior experience with Fallout to fully experience the story that will be presented.

 Yes, they have are open worlds similar in scope to each other.