You present it as though there were a choice. As internet access spread beyond a small number of geeks (and people started to buy stuff via the internet) then adverts began to appear in earnest and what you describe is more less inevitable.
This is true, it was inevitable, but you give the wrong reason.
Telling people (at least the non-tech "general public") not to use sites that have advertising is akin to telling them not use the web at all. When a platform becomes as widely used and powerful as the web then it inevitably becomes of interest to the rich and powerful who wish to control it.
No, the reason advertising was inevitable on the web has nothing to do with class warfare.
The real reason is that while it's practical to self-fund a small server in your basement, dorm room or university computer room that can serve static or semi-static content to a small population of users, it's an entirely different proposition to build and operate infrastructure capable of serving dynamic information to a billion users. Doing the latter requires tens of billions of dollars of infrastructure and billions of dollars of annual operation expenses.
Scaling the web up to where it could serve the entire population of the developed world, as it does now, required lots and lots of money. Where was that money going to come from? It ultimately had to come from the users, and there were really only two obvious ways for that to work: subscriptions or advertising. A subscription-based approach would have either placed barriers all over the web that made its core feature -- hyperlinking -- nearly useless, or else required the establishment of some sort of enormous micropayments system. But micropayments suck in all sorts of ways. I won't go into why because that's another (lengthy) post.
Advertising, however, has long proven to be the ideal way to fund large-scale mass media infrastructure. It made inexpensive newspapers possible, and then paid for free radio and television broadcasts, paying for armies of reporters and tens of thousands of local radio and TV broadcast stations. It works even better in the case of the web. It scales beautifully with the size of the audience, adds no friction to cross-site links and enables the economic creation and distribution of all sorts of mass-market content and services. Further, on the web it's possible to do targeted advertising, which increases the revenue potential and therefore decreases the amount of advertising necessary to fund the web (if you think there's a lot of advertising on the web now, be glad you're not seeing what it would look like without targeting).
Advertising also sucks. It gets in the way of the content that users are actually seeking. Advertisers devise and implement various tricks to make their ads more prominent than others, and more prominent than the content it's bookending. On TV, for example, ads are louder than most programs. Users develop schemes to avoid having to see the unwanted advertising content, and advertisers find ways to thwart these schemes. On the web, it's potentially even worse because of the possibility of malware getting inserted into advertising channels. And targeted advertising creates privacy concerns.
BUT the servers have to be funded somehow, and the old web model of donated equipment and bandwidth simply can't serve the entire population. And while advertising sucks, it sucks much less than the other alternative funding mechanisms.
So, advertising is inevitable. And given that there's a big money hose, it's then inevitable that the rich and powerful will be looking to find ways to siphon some of that money off for themselves. But that's an effect, not the cause, of advertising on the web.