That particular flash (the Polaroid-branded mosel in the original question) doesn't do wireless optical TTL; the built-in slave is just a triggering slave. There are third-party flashes that are compatible with the Sony optical wireless TTL system at nearly the same price point (this Cactus flash from Gadget Infinity† is an example; Nissin and Metz also have a good reputation for getting compatibility right). But there are significant limitations to optical TTL, especially when light modifiers are involved, since the flashes need to be able to see the triggering pulse from the flash connected to the camera.

Cable is an option, and there are third-party cables from reputable brands that are considerably cheaper than the Sony ones. They can be awkward to use, though, and daisy-chaining flashes to your camera makes it far too easy to take down the whole studio with one careless mistake.

At this point, there is no reliable radio-frequency TTL wireless option for Sony/Minolta. PocketWizard's Mini/Flex system only supports Nikon and Canon, and the Pixel King has been the subject of an awful lot of bad news on the forums (although it apparently works fine with older Alphas and flashes, reverse-engineering the entire feature set in a future-proof way is extremely difficult).

That said, a lot of the strobist mindset and technique revolves around manual flash rather than TTL. Any of the sync-only wireless triggers will work just fine with a Sony-to-ISO hotshoe adapter (they're pretty cheap), and that leaves you with a whole plethora of low-cost options. I know that David Hobby isn't a fan of the Yongnuo flashes (mostly for warranty reasons), but the well-respected pro brand Photoflex is (they offer the $50 YN-460II as the $150 Starfire). If you put aside the TTL requirement, you can get a hell of a lot of bang for your buck.

Frankly, manual with fully-adjustable flash is not a whole heck of a lot more work than TTL speedlights; it's just when you need to be portable (like doing event photography) that you hit the pain points and a TTL flash really pays its own way. You'll probably want to have at leaast one tilt/swivel TTL flash in your kit for those occasions. Both suffer in relation to "proper" studio lighting in that you don't have modelling lights, so there's a bit more experimentation in the setup and a lot more hit-and-miss in the actual shooting if your subject isn't static (you can't tell if a pose is going to cause a problem until after you take the picture).

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† I've had good luck with Gadget Infinity/Harvest One, and one of Canada's two major pro photo retailers, Henry's, has chosen to offer some of their Cactus-brand products for supported sale. (Where it doesn't interfere with other brand agreements, and at a considerable markup.)