Corporate pilot reported flying below the MVA for an area while conducting a contact approach. Pilot lost visual contact with the ground and flew an instrument approach to landing instead.

Narrative

I was at 3;000 feet and still couldn't see the airport but had ground contact so I requested a contact approach from Center and was cleared as requested. So I descended and turned towards the west to get under the clouds. Another controller came on and said I was below the MVA for that area and asked if I had ground contact and if I wanted to cancel IFR. I said yes and continued towards the airport. He said to contact tower but never heard from them and quickly could tell that I was going to enter the clouds if I continued so I climbed back to 3;000 and told Center that I couldn't hear tower and the clouds were too low and requested an approach. He stated that an aircraft had just got in front of me and tower heard me but they were offline. I said that I'm going to need an approach again and he had me turn to the north and gave me a squawk code. After landing the weather was reporting 900 [ft.] overcast. In hindsight I should have just requested an approach instead of trying to get below the clouds. It is a much safer option and would have saved time for all involved.