First things first. You currently own two scaling devices: the one in your TV, and the one in your DVD recorder. In most cases, the scaling included in the recorder (or player) will be of higher quality than that included in your TV, but it's not always the case - so first, try sending your DVDs in their unvarnished 'native' form into your TV, and see if you like the results. Then, apply video scaling using your DVD recorder. If the end result is better, fine: if not, leave it to your telly. In this case, I'd bet you'll prefer using the recorder to do the job, but you ought to try for yourself, just the same.
Second: scaling serves to match the resolution of an incoming signal to the resolution of a display device. DVD signals are 720 x 576, while your Sony TV is a 1366 x 768 panel, so as you suggest, scaling your DVDs all the way up to 1920 x 1080 (i or p) might not be of much benefit. You'll be applying a lot of work to one lower-quality signal to 'boost' it to 1080p, only for your TV to then rescale it back down to match its pixel count. The potential for error in this process - which you'll see on the screen, believe me - is considerable.
Scaling to 720p might be a better option, although even here, you're not actually matching your incoming picture signal precisely to the resolution of your display (because 720p is 1280 x 720, while as I said, your TV is 1366 x 768). However, at least you're getting in the same ball park. You'll also be supplying your display with a progressively scanned picture signal (1080i being interlaced, of course), which tends to produce smoother motion and less jaggies. Most of the time.