@mburnhors one of the elements of going into to a monastery is that you leave the worldly behind. The main part is your vocation and a life choice of living for Christ. Practical considerations? Most religious orders have their own economical structure implemented, in that they produce something or provide some service - you will be integrated into the structure of the order. Also, the nuns and monks lead a life, for the most part, detached from material goods…They have a few changes of clothes and a couple pairs of footwear. That is all they want or need. They are given their chambers, and the chance of living a life according to the rules of the order.
Health care, depends on the country. In some countries you have national health service and the religious are entitled to it as are all national citizens. In other countries there is collective health insurance, so you are covered and that fixed annual expense is shared by all members of the clergy.
As for dowry, it is far from essential and at maximum an accessory. I have known of nuns and monks accepted into religious orders that were deprived of financial resources. The question is only if this is what you really want and if you are not mistaken about your vocation.