Welcome! You should do what makes you most comfortable in the beginning. So many concepts/techniques are thrown at us at once, so if finger picking works for you – go for it.
However once you have overcome some of the initial hurdles, try incorporating the pick into your routine if the daily challenge calls for it. The brain is amazing and just using the pick for a few minutes a day will start training the brain to create the necessary neural networks. Take is slowly and remember you don’t have to be accurate or precise. Just play around with pick to get the feel of it in your hand and the movement. This action alone will develop the necessary coordination required. Brain neural networks are not created overnight so take it slowly.
Also, FYI – recently I met a guitar player who was in a motorcycle accident years ago. He was messed up – lost sensation in his hands, tremors, fractures, etc. Total wreck. His physical therapist told him he should pick up the guitar to help him recover and he did. Fifteen years later, you should hear this guy play – what an inspiration. So don’t let the tremors be a hindrance, but a challenge to conquer. Good luck to you!