The main problem is that betacam VTRs do not have firewire so there is no two way video/audio and no machine control. Machine control on betacam uses an RS-422 connection. Take a look at https://www.adobe.com/products/premiere/6cards.html to look at Adobe Certified Third Party Cards.
Also go to videoguys.com/vidcap.htm#firewire. Betacam video connections are composite, S-video, and component. The best quality available is component so if you want that,you will need a capture card with component inputs. Two cards with component inputs are ADS Pyro AV Link Studio API-757 for $640. and DataVideo DAC-1- for $660. I have not used either one of these or Decklink so maybe someone else can add their experience. I have a Sony PVW-2800 betacam at work that is similar to the 1800 but it is connected to a Media 100 system with a breakout box.
Audio out from betacam will use XLR connectors that can connect to your Mackie mixer. Be sure to look at machine control options or place the betacam deck so that it can be controlled from it’s front panel.
Rich Baim, ACE & ACI in Premiere Pro