Nibbling the elephant
I've seen a few stories on how he was caught and the biggest issue was reusing personas and his real name in a wide variety of places instead of keeping them all separate. Buying a laptop on Amazon wasn't something I remember hearing about, but was massively stupid. It would have been better to buy one used from a private party or at a computer swap meet paying cash and not generating any records. Lots of criminals that make piles of money often trip themselves up by buying expensive items such as cars that The Man tracks through registrations and taxes. Posh houses, boats, planes... anything like that is too noticeable to purchase with unclean money. A smart operator would get into a legitimate business and cook the books to show a nice profit, pay taxes on them all the while merely breaking even in reality. The company could then buy the fancy car and houses all above board without ringing any bells. The trouble is that the criminal wants to keep all of the money and not pay any taxes at all. Governments don't like that and have ways of finding people out when they make major purchases.
Getting a private server anonymously is not hard. I can go to the local mobile phone shop and get a new number and phone without having to show ID and just pay cash each month or pay online with a gift card purchased with cash someplace that doesn't have CCTV or poorly placed cameras where I can obscure my face with a hoody or wide brimmed hat. For fun, get a cowboy hat at the thrift store (if you never wear one). They have a large brim and you can toss it or drop it in a random donation bin when you are done. Get an email address from a free provider (not Google, someplace smaller). Take a drive to the country and find an out of the way address to give that will check out ok but since you will never get physical mail, that dog won't meow. The hosting company is mainly going to be concerned with getting paid. Once you are set up all you have to do is to keep the bill paid. Annual payments are best if you can afford them since discrepancies are less likely to trip you up as there will be no reason for any checking up, returned mail, etc.
Being near a train station is a good idea. You can do some war driving to locate open Wi-Fi nodes that you can get to with the train and log in from many different places as long as you're clever enough to watch out that you aren't putting pins in a map that describes the train route in an obvious way. Never, ever, ever be two different people at any of the locations where you're conducting illicit business. Some South American drug cartel leaders have pegged themselves by using a burner phone "for security" at a location and then making or receiving a call on their non-business phone in a short span of time. The cops then have another tidbit of information from that burner number and will track back it's purchase and activation plus any records, number listed in emails, texts, letters, etc.
Like a good actor, you have to be able to put on an whole new person and stay in character if you want to create something like the Silk Road. Break the 4th wall and you're nicked.