It is said that having two anti-virus software is bad for one's computer. But, I want to know if it is also bad to have an anti-spyware and a separate anti-virus at the same time. Should I just use the former that also offers anti-virus service but with a fee?
This is a mis-understood topic... (that I have probably also written wrongly in the past).
It is not bad to have more than one Antivirus on a single machine - it is bad to have more than one active scanner on a machine. It just happens that nearly every antivirus product out there that you purchase are active scanners - which is why it is easier to say that it is bad to have more than one antivirus on your machine.
The majority of spyware scanners out there on the other hand are just passive scanners and do not actually "hook" in to the operating system.
Personally, I would prefer a good all in one tool, however, you can run as many passive antivirus/antimalware programs as you want without problems.
(FYI, Malware Bytes have a free passive program, or a premium active program... Just use the free version).