Are you expecting such high levels of traffic that VPS/Dedicated are your only regular web hosting options? Because most sites do just fine on shared hosting, where you're not the one managing the web server.
And whether you're using WP, Typepad, or Squarespace, you're picking a SaaS (Software as a Service) provider. Their hosting is all going to be the same. You won't have access to real web hosting features like server-side scripting, RDBMS, shell accounts, etc. And these large blogging platform providers all have pretty much the same level of uptime and connection speeds. So if you're going to make your decision based on anything, it should be based on the software:
- How good (intuitive, powerful) is the interface? The interface is what you'll be interacting with, so this should weigh pretty heavily in your decision.
- Does it have all the blogging/CMS features you need? E.g. is it extensible enough for the type of site you want to build?
- Does the platform give you adequate room for growth? Will you want to expand to offer e-commerce or a forum? Will you want to integrate advanced analytics and lead generation systems 2-3 years down the road?
- How easy is it to export your data and migrate to another blogging platform? If you outgrow the platform or something better comes along, will you be locked in because all of your data is with this service provider?
Personally, I'd just get a good regular shared hosting plan for $8/month and have access to all of the features of the $36/month Squarespace plan and more. Most web hosts come with one-click installs of Wordpress anyway, so it doesn't take any kind of web development knowledge to be up and running with a full-featured blog in just 5 minutes.
That said, if you have fairly basic/standard blogging needs and don't need any advanced or custom features, and you're not that comfortable around computers, then it may be worthwhile to spend more to have most of the technical stuff hidden from you.
To have some of the more advanced sites showcased by Squarespace, you still need to have some technical knowledge or hire a web developer to work on your site, but for a basic blog site you could probably get by without one. And unlike getting a real web host, you won't have to upgrade the software yourself. It'll all be done for you. (Though, you can probably just hire some high school student to upgrade your Wordpress install every 6 months for $20.)