How to properly organize a technical support call center?

Question

Helpdesk

Colleagues, welcome! I really need your help in solving the problem, the background of which is:

• There is a call-center - 90% of incoming calls (~10000min\month);
  
• There is an old HelpDesk from HP - its task is primitive: creating calls, entering a unique ID, by which information about the partner from the database will be determined.
  

Problems:

1. You need to change helpdesk (saas) so that it is simple, convenient and beautiful - what do you suggest (maybe CRM is suitable?)
   
2. Do you need a virtual PBX, but there is no understanding of how it works - you only need the Internet or an IP gateway too (or will it work out with your own SIP) ?. Now the telephony is built like this - there is a router that receives the Internet and telephony from the Asteros virtual PBX, from it we go to the switch, which gives out 2 parallel channels - the Internet separately and the phone separately (they couldn’t set it up differently ... it works like hell , already tormented).
   

Accordingly, what other PBX to choose for our tasks so that we can somehow cross with HelpDesk (or with SAAS ty option?) And can we use the current Auvix IP phones or does each PBX have its own devices - do you have any suggestions?
PS I apologize for the inconsistency and confusion - I'm not strong in this topic and really need help, tk. I do not understand the principle of operation of voip and automatic telephone exchange.
Thanks everyone for any help!

Answer 1

Good afternoon.
1) From the free ones you can try OTRS www.otrs.com/. In general, their wagon and a small cart. From commercial before, I liked Kayako. Anyway, we ended up switching to a self-written system.
2) For a virtual PBX, only an Internet channel is needed. How everything will be set up inside you is the subject of a separate discussion. If Asteros did this, then they needed it that way, but this does not mean that it is correct and convenient.
Any phones/softphones with SIP support will do (IAX2 in some PBXs)