There are lots of highly unsuitable domestic fridges. It must be a Compressor version at the very minimum (those "bar fridges" are no good).
Ideally you want an A+++ or an A++ rating , but having said, my current fridge is just an A+ and I am truely amazed how economical it is for a Fridge/Freezer.
(word of note - the rating system is just changing to allow new products better than A+++ to be recognised and you will see old and new numbers quoted. Check if the rating of the Fridge being looked at is on the new or old system!)
PS. Unless you really want/need a Freezer, a straight Fridge will generally use half the power (I wanted a Freezer and have the battery bank to support that).
IMO, to run a compressor fridge comfortably, you need 100Ah of usable power (so 200Ah of lead, 100 of Lithium) to give you capacity for the fridge and using the camper normally (TV, lights, etc).
In the summer with decent weather, 100W of solar should give more than enough charge to compensate for the fridge.
When I did shows it would be Friday to Sunday off-grid - In the T5 I had a 12 Compressor Fridge, 200Ah of Lead AGM and 200W of Solar. I used to use a portable Induction hob during the day to make tea or soup to use the solar as the batteries would be fully recharged by 10 or 11 AM despite the fridge being fitted, lights used, etc, (I don't believe in switching off the fridge over night to save power - if you need to do that, your setup is wrong).
Right now I have an LEC T5039 135L Fridge/Freezer. It would be too large for a VITO though.
The previous Camper I fitted the Inventor 93L Fridge. TBH I think that could be too large as well. There is an Inventor 45L fridge with the same compressor and which is the same size as the popular Weaco CR 50 fridge. Both those fridges are very economical.
To give you an idea of power use, this is the SOC chart for my van for the last 12 hours where solar didn't figure
SOC went from 40% to 15% - a use of about 25Ah out of this 100Ah battery
View attachment 4564
But I have a fair bit of general power draw .... this is the same time range a few days earlier when the fridge was switched off ...
Start at 93% and end at 74% - a use of 19Ah
View attachment 4565
So on those numbers, My A+ rated Fridge/Freezer is using 12Ah ((25Ah - 19Ah)*2 for 24 hours) per day INCLUDING the inverter overhead. You can see the solar is doing nothing of note in the 12 hours of graphing shown.
(I don't know how it is so low, but it is - and the Fridge is down to 5C and the Freezer -20C, so being driven correctly.)