Short : No.
Unless you have many 1000's unorganized entry, and then, only an issue when displaying them.
Your favourites/bookmarks are stored in a folder or file reserved specifically for that use. There is nothing else there, and nothing else than your browser ever access them.
When your browser is not running, they just sit there unaccessed.
If you start to have to many of them, think about suppressing obsolete ones and organize the rest into a structure of sub-folders.
If your computer is on the lower end, Chrome may be a serious resources hog. In that case, Firefox is probably a better option. It also have addons available, several of them originally developed for Firefox and then ported to Chrome.
No mater what browser you use, install the AdBlockPlus and No Script addons. The first to get rid of invasive adds, the second to protect yourself from malicious and useless scripts. Both will make tour browsing faster and more enjoyable.
You really don't need to pay anything to get a very good anti-virus. The free Microsoft security, AVG, Avast and Avira are all very good options. Just don't touch the "free evaluation" offers.
The free version of Malewarebytes is a very good second anti-virus that need to be executed manually.
Install Spybot Search & destroy to get rid of non-viral pests like adwares and spywares. Be sure to use it's immunization feature. It prevent a lot of pests from even be able to install and run. To be run every month or two.
Ccleaner is a very good maintenance application. Highly recommended. Perform a cleanup every 1 or 2 week.
Regarding memory, if you have only the minimal amount, increase that to at least the recommended amount. It's the range where you'll get the most for your money.
If you have a conventional HD, be sure that it regularly get defragmented.
NEVER EVER defragment any SSD. Defragmenting those will adversely affect their performances and life span.