I retained my maiden name, and it was not a problem at all for my US immigration process. That I continued to use my maiden name was never even brought up at any part of the process. Note that I did list my husband's surname in the appropriate field on my NBI clearance, as you should too.
While it was no problem for US immigration, it has been an issue for my daily life here in the US. I actually prefer to use my married name, but because of my negligence, I was not able to renew my Philippine passport using my married name in time for my spouse visa interview. So now, my green card and SSN card list my maiden name, which means all my US IDs and accounts also list my maiden name. It will be a hassle to change all of them to use my married name once I naturalize.
So, if you prefer to use your married name AND you are confident that you can soon get a PH passport listing your married name, I recommend you use your married name as your current legal name on the I-130/I-130A and all other US immigration forms. List your maiden name (and any other names you may have used) under the "Other Names Used" section. It's ok to do so even if you currently have no IDs listing your married name. As @top_secret said, when it comes to changing your name for US immigration, the only ID that matters is the valid passport that you will bring to your visa interview. You will have around 1 year from I-130 filing date, to get a new passport with your married name. If for some reason you are unable to get a passport in your married name in time for your interview, the US embassy in Manila will not hold it against you for listing your married name on the I-130. They will just print the visa with whatever name is listed on the passport you submitted.