You've got your hands on a Dell Latitude E6500 which is a business geared machine/laptop. You can upgrade the ram up to 8GB's of DDR2 ram but in this day and age I think you'll have more issues finding a match pair. Yes you will need two matching sticks or a kit to ensure you don't suffer from incompatibility issues.
You could also go with an SSD, you can remove the optical drive and replace it with an SSD caddy and populate it there with a 2.5" SSD or you can keep the optical drive and then remove the original HDD and have the SSD there.
These links should help:
http/www.crucial.com/usa/en/compatible-upgrade-for/Dell/latitude-e6500
https
/www.amazon.com/E6400-E6500-E6410-E6510-Newmodeus/dp/B009OLHWNO
IMHO, you're trying to spend on a laptop that has seen more than it should and should only have upgrades done to it if the parts are, em, handed down.
Could you share the laptop's SKU with us?