You have to be Christian to be baptized. See [Acts 8:37]. Your translation may not contain this verse, but this is not justified. The "oldest and most reliable manuscripts" refer to those Greek texts prior to the sixth century, but Against Heresies 3:12:8 by Irenaeus and Treatise 12:3:43 by Cyprian, both from the early third century, cite it, as do several second-century Old Latin manuscripts, the earliest known Greek copy being from the eighth century. More likely, it was removed, as Erasmus states, by the carelessness of the scribes, ("arbitror omissum librariorum incuria.")
Once you are saved, though, you will automatically want to be baptized, and though it has nothing to do with your actual salvation, it acts as a testimony. No example in Scripture waited more than three days for baptism, (that was Paul in [Acts 9:9],) most did it immediately, and other than the thief on the cross, no believer in the Bible is known to have died without it. Do you have to do good works to be saved? Absolutely not, but they come naturally once you are.
We are commanded to baptize in [Matthew 28:19]. For examples of baptism for testimonial purposes, see [Acts 19:4-5] and [Acts 22:14-16]. Essentially, it is symbolic of the beginning of sanctification, ([1 Peter 3:21].) There are some who claim that it was a part of the transitional period (like tongues and exorcism) and is no longer to be done. I've already written too much, but the short answer is that we should indeed still be baptized as soon as possible but only after accepting Christ. See [Luke 7:29-30] for what refusal to accept baptism adds up to.