Decks, Patios, Porches and Docks - Picket Fence help

Ok, so I am wanting to put a picket fence around my new pond I put in a few weeks ago. I want it to be pretty sturdy to help keep my 5yr & 2 yr old from getting in there unattended. I have 4 x 8 foot sections of pre-assembled wooden fence. I will use to quarden off an area appx 20 x 25 feet. Here is my problem...I bought 4x4's for post and cut them in half making 4 foot high sections. If I set them 1 foot deep, do you think this will make a sturdy support. I will place them every 4 feet along the fence. If I could afford those fence spikes I'd get them because that seems like the best solution, but being a working mom...well, need I say more :)

Is there a way to make your own fence spikes relativaly cheap?? Would I be better off to wait until I can afford the spikes rather than doing all that work with digging & filling holes with concrete?

Thank you all for your help. I've only posted a few times here, but you guys always come through and it is much appreciated!

Super Day!
hps

I have put up a few sections of decorative picket fence last summer ( on a gradient which required i practically rebuild the premade sections) but living in PA with our super rocky soil and having just dug by hand more than my share of concrete piers i simply dug down about 12 inches but made the hole very wide. The wider it is the more stable the fence will be. I used the "lazy man" toss in and wet concrete and its standing fine to this day even after some 70 mph winds we had a few weeks back. Solid to lean against but its really for looks. HOpe this helps--Josh