Best CPU for LGA775 Socket in Dell Dimension E310 ?

What: I'm looking the performance of a 2005 Dell Dimension E310

Why: Computer is for a family member and it's fine for access emails and websites, but can't display video without incredible lag and low FPS. Twitch viewing is particularly poor. Also, I'm using this project as a learning experience but I'm stuck and hence this thread.

How: Since the computer currently has onboard video and only has PCI and PCIe X1 slots, a GPU upgrade isn't recommended. Therefore I've decided to attempt a CPU upgrade.

Question #1: What CPU's are compatible with this socket and computer?

Question #2: How did you come to this conclusion? I initially thought that I simply needed to only be concerned whether the CPU matched the socket on the motherboard. If it's not that simple, then what is the other determinations? Motherboard model or simply the chipset? I'd like to know for future reference; teach a man to fish kind of thing.

My plan: I plan on looking at a list of all available CPU options and then searching Ebay and seeing which processors are reasonable priced. I already jumped the gun and ordered a used Intel E6600 CPU for $5 off Ebay, before re-thinking that it may not be compatible.

Full disclosure: I started another message thread two days ago, where I was initially looking for a GPU upgrade, but realized that a CPU upgrade was the only way to go:

Dell Dimension E310 - Needs graphics card upgrade
http://www.tomshardware.com/answers/id-2971707/dell-dimension-e310-graphics-card-upgrade.html

Addendum: Current CPU is an Intel Pentium 4 521
 
Another point that I neglected to mention previously: I'm honestly not sure of the chipset in the Dimension E310. When I google it, I arrived at the following page: http://www.intel.com/content/www/us/en/support/boards-and-kits/desktop-boards/000005692.html

According to it, the Intel Pentium 4 670, is the highest CPU the motherboard supports. However, I don't know if this is the correct chipset, because I neglected to run a Belarc on the computer and it's not currently in front of me. I don't want to assume that my half-hazard google search is correct, but I thought that I should mention it. I'd appreciate help from anyone that has knowledge of this subject. Thanks.
 
The CPU's that are compatible with the LGA 775 the Intel (Pentium 4) and Core 2 Duo series of processors. The LGA socket does define the compatible processors.


Here are the LGA 775 processors available at Newegg.com. I wouldn't recommend getting a very expensive processor. You say it is a family memento. That will determine your budget that you want to invest.
http://www.newegg.com/Product/ProductList.aspx?Submit=ENE&Is NodeId=1&N=100007671%20600005851