Hello and welcome to Air Forums. I see this is your first post.
Your question about converters and batteries has many answers.
Most likely you'll want a multi-stage converter that maintains the batteries better than the old converter you're replacing. We installed a Progressive Dynamics 9260 in our trailer. There are lots of other brands out there.
Deep cycle flooded lead-acid and AGM lead-acid are good choices for batteries. I've used Trojans flooded lead-acid in the past and was happy. I'm considering Trojan AGM lead-acid or Lifeline lead-acid for upcoming replacements.
I know others will chime in here.
Lucius and Danielle
1992 29' Excella Classic
1996 GMC Suburban C2500 7.4L
2005 Chevrolet Suburban K2500 8.1L
Got a cooped-up feeling, gotta get out of town, got those Airstream campin' blues...