With a P4 you probably don't even have a PCI-E slot. So no 8800GT.

You could buy a 3850 but note you'd be buying into really old hardware and it'd be best just to overhaul what you have completely.

There is no such thing as a "gaming monitor" - just grab a 19" LCD with a 5ms response time and you're fine.

I can relate to this comment because it's what happened to me.
I had a P4 2.8 ghz and an AGP ATI x800.

I upgraded my monitor to a 22" widescreen.

Needless to say Windows was fine but I didn't even have close to the hardware to run many games on that monitor (although Sins ran fine for the most part). Ended up just building a new computer and I'm much happier now.

And just to note on my system I did run it lower then native but still at 1440x900. I turned off AA as well as in game things like dust, debris, elevators and bloom. The x800 kept it up around 30 fps except in intense battles where it would drop to 10-15. But it was still very playable. But it's so much nicer now.

By the way the reason I upgraded was actually Oblivion. It looked so bad at anything less then 1440x900 and at that resolution I got about 10 fps and that's with things at low. Unplayable. On my new PC it almost never drops below 60 fps and that's with everything cranked up to max. Amazing difference.

So I think it really all depends on what games you are playing. If you have the money to more upgrades if you need to then I'd say go get that monitor and see how your games perform. If you can't run them well then do more upgrades as needed. But Sins should be fine if you turn down some stuff and run at lower then native resolution.

It very much depends on your budget, and what motherboard you currently have.

Personally I would go with something along the lines of a RAM and monitor upgrade, since RAM is currently very cheap, and a bigass monitor is really sweet.

I myself have two systems:
P4 "Prescott" 3ghz with 2gb DDR2 667mhz and a GeForce 7600GS. This system can run sins with all settings at full (including AA) at a resolution of 1680x1050. stable at around 30 FPS.
My other system is a P4 "Northwood" 2.66ghz with 1gb DDR 400mhz and a Radeon X800XT AGP. This system is badly hurt by my motherboard only supporting AGP4x though, and as such can barely even play sins at all, even with everything set to lowest in 1024x768.
This shows the importance of a balanced system. Even if the names of your components are good, there might be a bottleneck somewhere to f*ck it all up.

But back to you. In order to help you in a better way, I would like to know a few things about your motherboard. Such as: What socket it is, what DDR version it supports (DDR or DDR2) and what graphics interface it has (AGP or PCI-Express).

Also, as some people here have pointed out, a change in monitor is also a change in the native resolution your system has, and as such it will take more processing power to calculate all the extra models and textures that can be shown at the same time.