According to EveryMac, your serial number is a 20" Early 2008 iMac:
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iMac "Core 2 Duo" 2.4 20-Inch (Early 2008) 2.4 GHz Core 2 Duo (E8135)
Intro. April 28, 2008 Disc. March 3, 2009
Order MB323LL/A Model A1224 (EMC 2210)
Family Early 2008 ID iMac8,1
RAM 1 GB VRAM 128 MB
Storage 250 GB (7200 RPM) Optical 8X DL "SuperDrive"
This generation can be updated to 6GB PC2-6400 RAM (2G + 4G sticks). It's physically possible to install 2x 4GB sticks for a theoretical 8GB, but Intel's controlling chipset for the CPU won't acknowledge or use the last 2GB*.
iFixit has both chips in stock:
PC2-6400 2 GB RAM Chip
PC2-6400 4 GB RAM Chip
iMac Intel 20" EMC 2133 and 2210 RAM Replacement
If you go looking for this RAM on the used market, be careful to look for PC2-6400 SODIMMs, which are much less common than the slower PC2-5300 SODIMMs and the faster PC3-8500 SODIMMs. The PC2-6400 generation was pretty short; it was used only in the Early 2008 iMacs and the Early 2009 MacBooks, and wasn't around in the Windows marketplace for much more than a year.
As far as brands are concerned, I'm much less fussy than I used to be. Samsung chips are normally regarded as the gold standard, but a lot of RAM companies use Samsung chips. When you're buying new RAM, you should always buy from a retailer that offers a lifetime warranty; RAM does die occasionally, and it's better to have a commitment to replace. Brands that you typically see installed as OEM by Apple with Apple's stickers on them are Samsung, Micron, Hynix and Elpida; these sticks are available rebranded from all sorts of retailers.
I tend to buy my new RAM from OWC in Illinois; they've been a Macintosh-market retailer and manufacturer for nearly 30 years, so I can be reasonably confident that they'll be around long enough to answer a warranty claim - they're not going to disappear before the "lifetime warranty" has gotten close to what I consider an appropriate length. They have excellent customer service, and the people who answer the phone are tech-savvy.
*Computer industry fun fact: The Intel memory controller limitation was universal in Core 2 Duo computers of the era, but most of the big manufacturers (Dell, Sony, HP, Gateway, Toshiba, Acer etc) were perfectly happy to sell you 8GB of high-priced RAM, even though the last 2GB were a total waste of money. Apple was the one major manufacturer that refused to offer the useless expensive RAM as a build-to-order option.