Is spybot still necessary to have?
You need antispyware protection.
Or you take Spybot, or Lavasoft Ad-aware, or Ewido, or A-Squared, or Spyware Terminator. All are free.
It's good if you have SpywareBlaster with any of the above.
Is my system going to have enough protection with M/S Firewall & Avast?
Well, a firewall (inbound and outbound) won't be bad.
If you can, try, Comodo Firewall, or Kerio, or ZoneAlarm, or Jetico. All are free.