How should I phrase "Not only but also.."?

This sounds better to me:

I bought the Dell laptop not only because I found the price appealing, but also because I liked the fact that the laptop had an integrated webcam.

I just moved the 'not only' up front. This pretty much cascaded to all the other changes: not splitting up "but also," keeping the tenses more consistent ('I found' vs. 'did I find'), etc.

Is my use of ".. not only .. but also ..." appropriate?

Your phrasing sounds grammatical and idiomatic to me. I believe it is correct.

Is there a better way to phrase such a sentence?

There is a stylistic tradition in English for brevity. This is often promulgated by the famous dictum “omit needless words”. It may be that your sentence does not sound right to you because of the large number of words used to express a simple idea. Following that school of thought, you could try something like this:

I bought the Dell laptop for the price and the integrated webcam.

The brevity rule—like all style rules—is controversial, and many of the ideas from your original version that I have left out may have been necessary and intentional. The best sentence for this situation is likely to be something between your version and mine.