That laptop is from around 2011/12, so the CPU cooler could be clogged up with dust and dirt, killing performance as the CPU tried to keep itself cool. There's a program called CPUID HWmonitor that will tell you the processor's temp in real time, download it and run it, and see what the processor is running at. For a laptop CPU max temp is 100*C (for Intel) and should normally be running "up to" 70-80*C, get into the upper 90's and it's going to thermal throttle, and run sloooowww. If you're not scared of ripping apart the laptop, you can clean the CPU cooler, just need some small screw drivers, thermal compound and alcohol to clean off the CPU and cooler. Look at Youtube for your laptop as they probably have a tutorial on how to remove and clean the CPU cooler. I have done several, and most of the coolers were clogged up to varying degrees. I think it was Boomyal had the same problem you're having, and it was a clogged up CPU cooler.
How much RAM does the laptop have now? If you're running 32bit OS (IE: Windows 7) the max RAM is 4GB and I would have that amount. If it's a 64 bit OS, you could get away with 4GB, but I'd run 8GB. (I just checked the PC I'm on and it's using 4.2GB of RAM, and the PC isn't doing much right now...)
SSD's are nice and I have them in all the PC's/laptops at our place, but once the computer is up and running it's not like night and day. Booting, shutting down and opening programs you'll see a big difference, but general surfing the web, it's not going to do much. That hard drive (if original) is 6+- years old, and probably on borrowed time, so a good reason to swap it before it takes a dive. SSD's are kind of spendy, but get a good one if going that route, Samsung EVO 850 or one with good reviews, lots of garbage SSD's on the market. I have picked up several 500GB Western Digital WD5000LPLX 500GB "Black" hard drives off Ebay for $25-30 that were new laptop "pulls" from people who upgraded to SSD's on their new laptop...
Formatting and reloading OS can help as Southkogs mentioned, and I have seen improvements from that also.