I believe the best option to be: additionally.
So:
Support for the arts would be very important in my utopia. Museums and art galleries would be provided with adequate funding. Additionally, free concerts would be sponsored every weekend to encourage culture in the community.
The other transitions wouldn't work as well:
- First would indicate the sentence is enumerating the first one of a list to be mentioned. In the excerpt, the sentence to be introduced is presenting not the first, but the second item.
- Finally, as redundant as it may seem, introduces a conclusion. It may also introduce the last idea of a list. In this case, there is no list, only two things mentioned, plus the second sentence does not conclude what was said in the first one.
- In particular could be used if the second sentence were explaining, restricting, a detail about the first sentence, which is not what we see here.
Therefore, the best option is additionally, since it makes it clear that, besides what is stated in the first sentence, what is said in the second sentence will also happen.