<<or to learn Swiss German/Basel style>> makes me laugh - sorry :)
Basel is a city just at the border to Germany as well as to France (the only German (and of course French) speaking part of that country). I think the best for you is brushing up your French since in Basel people are used to speak French beside Baseldiitsch and German.
btw, you would have no problems only speaking English there, because Basel is a quite international city due to the two well known pharma companies Novartis and Roche and the chemical industries Ciba and Clariant.
coming back to Swiss German/Basel style; you would have a hard time to learn it, because that language is pretty "colored", i mean it has a very unique accent.
let me tell that Swiss French and France French is very similar although French people say there are some little differences but the understanding between them is absolutely no problem.
BUT, between High German and Swiss German the differnce is that huge, so a person from Berlin is unable to understand Swiss German but a Swiss understands High German. this is due to the fact that Swiss German is hardly a written language because of the many different dialects in Switzerland. the vast majority of books and ALL newspapers in Switzerland are written in High German (except of course those in the French and Italian part of Switzerland).