When you load a new Web page in your browser, that page is downloaded into your computer's memory not your ssd. If that page contains data that requires a lot of memory such as high resolution graphics, more memory and more time will be required to store that in the main memory of your computer. The time to transfer the data from the Internet to your memory is dependent on the speed of yourcpu and how closely that speed matches the speed of your computer's memory. Almost all modern computers can transfer the content from a Web page through the processor to memory faster than the Internet connection can deliver it. Even a 5 Mbps connection cannot feed data fast enough to keep a 1-GHz processor busy for long.
Internet providers often recommend a specific minimum memory size for reliable Internet access. This doesn't mean that all of that memory is necessary for browsing the Web, but low memory can have an indirect effect on your experience. All open programs will utilize some memory. If your main memory is nearly full and you try to download a Web page with your browser, your computer may have a memory management conflict. This will require that your processor move the main memory's contents to a different location in main memory. There is also a possibilitythe contents may be moved to disk memory.
EDIT - I just did a little experiment. I opened Internet Explorer. Then I opened 100 tabs in the browser. Each tab has a different web page. I also listened to my favorite Internet radio station, used a photo editing application, and several utilities to help keep track of cpu load and temps. Each time I opened a new tab the load on one of the cpu cores would spike for a second from 1% to 7% load. There was no significant increase in cpu core temps.
When it was time to close all 100 tabs I had a choice. I could either close one tab at a time or I could close them all at once. I chose closing all tabs at once just to see what would happen. It was amazing. All 100 tabs closed in the blink of an eye. The cpu very briefly spiked to 18% load and cpu core temps hardly changed. No muss! No Fuss! No bother.
The problem with my experiment is that it is flawed. Trying to compare your pc with my pc is like trying to compare apples and oranges. I've got a high end Z97 system with an Intel Core i7 6700K Skylake cpu, 64GB of memory, and a Samsung 840 EVO ssd for the primary boot drive. I also forgot to check ssd activity so I don't know if any of the web pages were moved to the ssd.
It definitely would not hurt to have an ssd instead of a hard disk drive. An ssd will usually improve overall performance. The improvement is quite noticeable when switching from a hard drive to an ssd. The upgrade from hard drive to ssd is definitely worth it.