Who's order if filled first.

I have an order in for 300 shares of sprint and so far only 81 have been filled. My question is how is the rest of the order filled. For instance do we have a waiting place where 500 people are trying to buy this stock at the same time and we are all line getting bumped to the top like first come first served? Or what says scottrade is filled first before we go to another broker and wee what they have.

Finally executed note time diffenence
S - 11:43:38
Bought 219s @ $5.62 - Total: $1,230.78


S - 11:03:41
Bought 81s @ $5.62 - Total: $461.22

I'm guessing you mean 10:43 and 10:03 EST. At that time the mid market was $5.625 so yours was getting filled whenever someone was willing to sell for $5.62. Scottrade has nothing to do with whether or not your order gets filled. They just put the order through I'm assuming for BEST market....TDA allows you to select which market if you want but usually you get better and quicker fills using BEST.
Also you were at a further advantage in that the retail customers get preferential fills and 100 lots get preferential fills but then your just in line with others making the same market with the same preferences.
If you wanted an immediate fill then you would have had to bid $5.63 and probably been filled at that or $5.625 as there were plenty of sellers at that level.
At 10:43 EST there was a bump in sell volume that filled everyone at that level then by 10:44 the market shifted to a bid/ask of $5.62-5.61 with mid market fills of $5.615.

So if I want to buy or sell 300 shares (all or none) it would be better to put in a order for 300 all or none than just a order for 300?

If it's a limit order...yes. I guess if it's not a limit order it doesn't matter..heh.

It's not something I personally would worry about as a partial fill at a lower price would be a high class problem.....as if the price moves away and you don't want to own an odd number of shares...guess what? You get to flatten the position for a profit.