Should I install any third-party software to speed up my computer?

In general, no. Most third-party software that claims to improve system performance is either ineffective or can actually cause more harm than good. The best way to speed up your computer is to regularly maintain it by cleaning out temporary files, defragmenting the hard drive, and more. Free tools like CCleaner and Auslogics Disk Defrag are good, safe options for this purpose.