My favorite part of my TV’s remote control is its “menu” button. Not because I enjoy adjusting system settings–I get quite enough of that on the job–but because pressing that control takes me to this Sony’s collection of Internet-connected media apps.

Between Netflix and Amazon alone, we can easily spend as much time watching TV over the Web as we do over the air. (We canceled our TV service back in 2009.)

Even for the vast majority of TV viewers who have not cut the cord on cable or satellite, “connected” has become a major selling point. Some people call these Internet-linked sets “smart TVs,” but you could argue that eventually we’ll just call them “televisions”: The NPD Group’s DisplaySearch unit estimated in November that 27 percent of all flat-panel TVs sold worldwide last year would have some level of Internet access, with that number hitting 54 percent by 2015.

For now, though, “some level” covers many different things. Most connected TVs, along with connected Blu-ray players and other under-the-TV boxes that stream Internet media, sacrifice compatibility for simplicity. They’re less work than tethering a PC or Mac to a TV, but they can only connect to a site or service if they offer an app for it.

(You don’t have to like that trend. But with the failure of Adobe’s efforts to turn its Flash format into a common language among living-room hardware, you’re stuck with it anyway.)

That means these connected devices’ menus don’t all offer the same entrees. After Netflix–a service so near ubiquity that it’s campaigning to have its own button on other vendors’ remotes–the selection quickly gets less consistent.

YouTube would seem like an obvious call, but it’s absent from Roku’s otherwise absurdly-comprehensive Web receivers (although the company says it’s working on that) and Vizio’s sets.

Amazon’s popular video-on-demand service, in turn, gets a prominent spot on Panasonic, Sony and Vizio TVs and Roku boxes but not the Apple TV, Sharp’s sets or recent Samsung models.

Hulu’s Hulu Plus service, a newer entry in the Internet-video market, has a home on some LG, Panasonic, Samsung, Sony and Vizio TVs, plus Roku devices, but not the other hardware noted here. A similar pattern holds with YouTube rival Vimeo and Netflix competitor Vudu and the video services of Major League Baseball, the NBA and the NHL.

Those sports sites, unfortunately, usually limit real-time game watching to people outside of a team’s city. ESPN, in turn, only offers its ESPN3.com service in app form on Microsoft’s Xbox 360, although Google TV owners can watch it using that system’s built-in browser.

(I often hear from readers who want access to the major TV networks’ own sites. But since those companies usually block Google TV users from watching video clips there, the odds of them providing connected-TV apps look poor for now.)

Things are even less settled outside of video. The Pandora Web-radio service may be on its way to securing a spot in every other car stereo, but among these vendors only LG, Roku, Sharp, Sony and Vizio tout support for it.

I suppose this disarray shouldn’t be a huge surprise in a category of hardware that didn’t exist six years ago. But in the interest of speeding up this evolution, I have three suggestions for the industry:

One: Social-networking sites belong on your small screen, not your big one. I don’t get why so many connected sets provide access to either Facebook, Twitter or both–don’t most buyers of such hardware already own a smartphone or tablet that provides better access to those services?

(Maybe I’m just old. If there really is demand for reading tweets or Facebook status updates from across the room, please inform me via telegram.)

Two: We need better home media-sharing options. Outside of the Apple TV, playing your computer’s photos, music and videos generally requires setting up DLNA (short for Digital Living Network Alliance) file sharing.

This can work reasonably well in Windows, but Mac OS X doesn’t support DLNA without assistance from third-party software. And in either scenario, it falls short of the simple, reliable synchronization I saw when I tested a Squeezebox music player eight years ago, which used a simple bit of add-on software to simplify complicated media sharing.

Three: If nothing else, can manufacturers at least agree to provide searchable, sortable lists of their connected devices’ Web-media apps on their own Web sites, so shoppers can know what they’re getting and buy accordingly?