UK immigration to USA through marriage

I am planning to move from England/UK to the USA. I am from the UK and I have been with my girlfriend from the USA for several years and plan on getting married as soon as possible for immigration via a courthouse marriage. I am about 60 days of the 90 days through the ESTA travel visa. We already have the marriage license. Is it okay to still get married ASAP while I am still working on the paperwork for immigration (ex: I-485, I-130, I-765, I-864)? I have my health exam next week. I should have it done before the 90 days are up. I am just wondering since it might be risky if the 90 days are over and then I have to fly back to my country so I don't overstay in the case that the paperwork is not done by then. If so, am I able to visit again easily with the ESTA despite being married to a US citizen? Then continue the paperwork after being married when in the possibility I have to come back?