Virus
A computer virus is a form of malicious programming which enters your computer system without your consent and attempts to replicate itself on other computers.  There are a variety of ways in which they can do this including, infection of files, macros (in Word or Excel files), and web browser hijack.  A virus can even infect a web servers and spread itself onto a computer that visits the page.  Some virus programs have been done almost by accident - where the author didn't expect it to propagate so much as it did.  Many have been created just to see if it was possible or to be a nuisance.

Adware
Adware is software designed to generate revenue for the author.  While not a virus, it isn't exactly honest.  Adware usually piggy-backs along with a desired software or somehow tricks you into installing it.  From there, it may produce pop-up advertisement windows while you browse the internet.  It might use the Windows notification area to show blatant advertisements.  To trick you into installing them, they might disguise it as cute and friendly app or a helpful add-on. 

Malware
Malware is a blanket term to describe software that is designed to disrupt, damage, gain authorized access, or exploit a computer system.  The software's motive can include extorsion: a crypto virus can encrypt your personal files and demand some form of untraceable payment as a ransom to unlock them.  Unfortunately, some individuals or companies pay this ransom, but there is no guarantee the other party will "unlock" the data.  They are pirates, after all.

Some malware apps are part of a botnet; they make your computer act as an agent (robot) for a master server.  These might consume some of your CPU time to compute things on their behalf, or they might use your computer to send data packets to a site they wish to attack.

Malware usually needs some sort of trickery to get onto your computer.  They may start with a pop-up telling you an infection is detected (bogus) prompting you to click through to try and resolve it or make the pop-up go away.  The chain of events unfold from there.  Many of these lock out your ability to use your computer and are quite difficult to remove.

Opinions vary and each situation is unique, but we tend to say there is not a need to rush into changes.  If it isn't broken, why fix it? 

Granted, over a long enough time span you probably need to update your operating system to something newer.  The improvements are gradual.  We don't recall having seen any world-changing features or capabilities from one to the next.   

Upgrades are needed to maintain compliance in several regulated industries, but a lot of the time you can simply get the new version of Windows when you buy your next computer.  

Computer slowness is a frequent symptom of malware, but that is far from the only reason. 

There are frequent updates to operating systems and applications.  This additional software means more lines of code.  The software evolves and gets larger but the hardware remains the same.   Over the life cycle of a computer, it often makes sense to increase the RAM or transition from a spinning drive to solid state.

General slowness can also be a symptom of a failing drive.  Drives fail in different ways, and sometimes they become very slow.

Overheating can also manifest as slowness, especially in laptops.  Mobile CPUs are designed to throttle back if they reach their thermal limits. Unlike desktop computers, laptops haven't the extra margin to tolerate blocked cooling fins or dust-caked fans.  Sometimes compressed air solves a lot of problems, but care is needed to avoid breaking fan blades.

There is not a single answer to this question.  The procedures vary quite a lot with the type of infection, and which operating system it is.   The countermeasures also change with time.  What worked best five years ago may be obsolete today.

For moderate infections,    Emsisoft Emergency Kit and  Malwarebytes Antimalware do a pretty good job and have free-to-use versions.

There is not one program that gets everything. 

In our repair shop, we spend a lot of time refining our list of removal tools and an order of operations.  Some produce best results in safe mode, others in normal mode.  Some apps work well in one version of Windows but break something in another version of Windows.