I had a Tamron 28-300mm VC f/3.5-6.3 (model A20) as my first lens, and wouldn't particularly recommend it, I'm afraid, though I'd still be inclined toward a similar superzoom as an introduction - having such a wide range of focal lengths is useful in letting yourself know what ranges you actually tend to use. In my case, it wound up being primarily as wide as it'd go, for landscapes and portraits, and as long as it could manage, for wildlife - the next lens was a Nikkor 300mm f/4D, with quite outstanding clarity, contrast, and lack of CA.
What put me off? As above, a lot of my use was at 300mm - if you're not concentrating there, it's a very different story. At 300mm, it's rather soft, and prone to chromatic aberrations. At the other end, however, it's nothing to grumble about at all.
I'd say the thread title isn't quite specific enough. Every maker has stronger and weaker lenses, with Tamron producing some quite acclaimed models - but their 28-300mm ones aren't amongst them. But, as above, if you're only occasionally using the long end, it might in fact be quite a good option, and an economical one.
As a side note, all things being equal on that model, I'd go for the one with a good warranty. Unfortunately, I bought mine before they extended it beyond one year. Not long after it expired, so did the lens' optical stabiliser and autofocus, which would cost some £240 to repair - about the cost of a used one from the likes of
MPB.
If Tamron's superzooms remain tempting, you might also consider the difference between the PZD model(s) and the "conventional" motor models. The A20 used the latter, making it relatively loud in operation - nothing that'll scare wildlife, but an obvious, pronounced whirr/buzz. The later PZD models are, I'd imagine, as quiet as any other ultrasonic motor lenses.
