I don't mean to sound mean, but your questions suggest you may want to reconsider building your own machine for now. Nothing more frustrating than trying to assemble a (relatively) complex machine with lots of things that can (and probably will) go wrong when you don't know at least more or less what you are doing.
From what I understand, motherboard=monitor fps performance based on resolution. That correct?
My maximum resolution is 1650x1050 (if Im remembering that correctly) so what motherboard would be needed to run such a resolution smoothly?
Your motherboard won't be the deciding factor in resolution, the graphics card will be. I'm not sure there even is a motherboard currently capable of driving a 1650x1050 display at 60 frames per second on a higher end game without a dedicated graphics card. If you only want (ever) to run at 1650x1050 then you're not going to need a super high-end graphics card. Check out this article for performance ideas and what is a decent "bang for the buck" card in a variety of price ranges (you might do fine with a card under $100 at 1650x1050 for most games.)
Actually, let me step back. Some basic terminology:
Motherboard - This is the heart of your computer. The CPU sits on it as does the computer memory and I/O buses that communicate with your storage devices such as hard drives, external USB devices and mice and keyboards. Nearly all modern motherboards also integrate AUDIO into the motherboard, so generally you will not need a dedicated sound card. Many motherboards also integrate VIDEO onto the board. This is fine for low-end applications under some circumstances, it WILL NOT generally work for gaming. Not every CPU can fit into every motherboard, far from it in fact as the motherboards have whole hosts of chips dedicated to working with specific types of CPUs and the CPUs themselves have particular socket size requirements.
Graphics Card - This does the rendering for your display. The resolution the card can support will be defined by the memory on the card. The FPS it can churn out will be defined by the power of the GPU (graphics processing unit). Any gaming PC is going to want to have a Graphics Card in it. This will plug into (physically) a slot (or slots) on the motherboard.
Memory - There are several kinds of memory in your computer. The SYSTEM memory is located (plugged into) your mother board. This is used by the operating system for running programs to store temporary data (such as programs, program data, etc.) The GRAPHICS memory is housed on the graphics card (though if you use onboard graphics rather than a dedicated card, the SYSTEM memory will be shared as GRAPHICS memory.)
Hard Drive - Connected by cables to your motherboard, they store persistent data that needs to be kept even when the computer is not turned on.
CPU - This is the brain of the computer (Central Processing Unit) that executes programs in memory. It sits on your motherboard.
Power Supply - This converts the alternating current that comes our of your wall socket into the direct current that all of your computer components need to use for power. You'll need one big enough to power all the components in your computer at full load simultaneously with room to spare "in case."
Computer Case - This holds all of the components inside. It has to be physically big enough for everything to fit inside and well enough ventilated to make sure the components will not overheat. This isn't as trivial as it may sound. Certain cases are designed for certain "size" motherboards. The most common form factors are ATX and the smaller Micro ATX.
Soooo.... when you are building a computer "from scratch" you are going to be buying a number of things:
- a case
- a compatible sized motherboard
- a CPU that is compatible with the motherboard (if it did not come bundled with the motherboard)
- a graphics card that will work with the motherboard and case
- a hard drive (or SSD if you want to get spendy, either way, it is persistent storage)
- memory for the motherboard
- power supply
- input devices (keyboard, mouse)
You may know all of this or none of this. I hope it is of some use, you seemed a trifle confused on "what does what" from your questions.