I can't help but to comment. OP, marriage is not a short term matter, marrying Indonesian is not as easy as it seem. I know a lot of Singaporean did it, married by Islam law in Batam and never do any ROM. The thing with this path, it will affect the wife and the children status in future, I definitely against this path. If you ought to register officially (ROM), it will be better if you do it in Singapore, and I suggest you go on this path. Think again and consider the consequences, have you not read on the newspaper about those wife from Indonesia whose children can't even come to Singapore? I also know few wife who forever can't get LTVP what more PR in Singapore, including their children. How about housing? How you going to get a HDB if you unable to fulfilled the basic criteria? House in Indonesia. foreigner can only purchase it if they married to Indonesian and in the event of divorce normally the law not as fair as in Singapore, possibility the property
will be given 100% to the Indonesian pretty high. And also the lease of land in Indonesia only 25 yrs, the owner need to renew it upon expiry (or the land can be taken by government if they deem they need the land), it make the price of descent house expensive, now resale market price in Batam for a descent 2 bedroom house in city is around 80k and need to be paid by cash, no bank loan given to foreigner and local who do not draw salary at certain threshold.
Indonesian who wish to work here must get at least Spass, no work permit unless they are FDW. And for foreigner to reside in Indonesia also will cost a lot of money, to work there possible but not easy to get employer who willing to pay the Foreign Employee Tax unless hiring you in their top priority list. You can go there as an expat, but this route will need special skill / talent and company must justify to the local government there on hiring foreigner. You can check how much it cost to get KITAS, it's a LTVP Indo's version, need to renew yearly, if you go through the normal process I think it will be less than 2 milion IDR, but normally people will go through "middleman" and the price and be sooooo marvelous.
Just ROM in Singapore, you no need to convert, just keep your own faith and she can keep hers, the marriage certificate from here is acceptable in Indonesia, there are MANY different faith couple registered their marriage in Singapore, those you can easily search on Google were the celebrities for example.
After write such long comment, once again think through before the decision, I also have bad news for you, normally the man need to support not only the wife, sometimes need to support the whole family and extended family, unless she is rich of course. Be ready mentally and pocket-tally