Getting married here poses no problem in of itself. However, staying in Singapore could pose a problem.
She can file for a marriage license and you both will need to go the the
ROM (Registry of Marriages). Have a read of the link and you will be okay in that regard.
You will, however, have to sign a statement to the effect that you understand that the marriage WILL NOT confer any special privileges with regard to Visas to stay here. That is the Purview of the
ICA (Immigration & Checkpoints Authority and an LTVP is not a guaranteed thing. You could conceivably find youself in the precarious position of being married but not allow to stay here. This is especially so if you were to start doing runners to Malaysia and/or Batam to get a new tourist visa (SVP).
That still will not allow you to work. In order for you to work you would need your prospective employer to file for an
EP ( employment pass) to allow you to work with THAT employer. If lucky, you may get one and be allowed to work for that employer only. If you change jobs, you lose your EP and will have to reapply for a LTVP as you will be only given a 30 day SVP after the EP is canceled. There is an LTVP+ now available which will allow you to work, but you have to be married for a minimum of three years before ICA will entertain giving you one.
It would probably take a minimum of two to three years working here in order for you to apply for PR under the Professional, Technical Scheme (PTS) Under your wife's sponsorship under "Family Ties" scheme, it could happen earlier but only provided her income is substantial enough to warrant the ICA's approval (generally around 2.8K/mo).
After you have digested all that is on the three links I have provided, if you have specific questions feel free to ask, we will try to help.
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