The initial payment of three times the rent is standard and covers the deposit and attorney or realtor fees I believe. If it's too much you just need to look somewhere else. there are many place around the perimeter of Santiago where you can get a house for RD12-15k a month. Otherwise an apartment is an option and they go for 8k to 12k for a nice 3br one.
They cost more if they are furnished and usually the fee for the lawyer is the same to one month rent and in other cases around 5,000 pesos. The owner of the property wants a security deposit (like 1 or 2 months rent) just in case you break something in the property or you decide to stay a couple more months without paying, that happens very often to homeowners they rent and then the people don't want to leave.
My parents have an apartment in Santiago close to Cerros de Gurabao where I used to live and now is rented for 6,ooo DOP to a friend. The apartment has 3 bedrooms but the third one is small passing the kitchen next to the laundry area more like a maid bedroom. My neighbor on the second floor lives in the states and was renting hers completely furnished for 600 or 800 USD. I don't know if she still wants to rent it. The neighborhood is very quiet and close to everything. Los Jardines Metropolitanos always offer apartments for rent half or full furnished