Dedicated (leased) servers are a good high-end option if you really need that. But you don't, judging by the scenario(s) you've described. That would run you $100/mo and up - about $250 if you want a "premium" unmananged system with relatively high-end hardware and a decent bandwidth allowance. Comcast Business Class also offers fairly high bandwidth connections that you can get to your home if you tell them you have a home business. 50mbit/s download, 10mbit/s upload, that will run you about $200/mo. My old office had that connection and the advertised speeds were pretty close to reality. Back that up with some decent server-level hardware (about $2500 per server for a dual CPU system with 8-12GB of RAM and a 4+ drive RAID 5 array with hardware RAID controller). But again that's all massive overkill.
What exactly is a "headache" about normal web hosting that has you willing to spend so much money and time and effort to learn such complex systems and manage and troubleshoot them? People are paid good money to do this professionally because it's a complex, skilled job. Like mouser said, ask gothi[c]. DC runs some mid-range(ish) servers (2 I think) and it's a decent amount of work just keeping them going in top shape. You have to worry about OS and software updates, security issues, installing and configuring all your own server software and support packages, etc, etc. These are good skills to have so if you have notions of actually going into that professionally it would be worth learning. Otherwise I'd say don't bother. If you're unsatisfied with traditional shared hosting due to resource issues or downtime, spend your money on a good VPS setup or fully managed dedicated server, let them deal with all the hassles while you enjoy high reliability and excellent support. For a decent managed VPS you're looking at maybe $50-100/mo. For a dedicated server $200-400, depending on hardware, support level, etc.
P.S. I agree, if you have $20k to spend on just these web projects, send it DC's way. I guarantee mouser will find a way to provide you awesome, reliable server space for life, and do a whole lot more with the money to boot.