For guided walks, the best base would undoubtedly be Puerto de la Cruz. There are mostly German companies running hikes in the Anaga + Masca regions. Try these places as a starting point:
Stan and Eve run KWA guided walks, which is a well-established business based here in the North of Tenerife. They've been operating successfully for almost 15 years and even have their own coach (unlike a lot of the other companies who use the local buses). They are Winter resident guides.
You'll also find lots of further info on their site.
http://www.kwa-guiding-tenerife.com (Puerto de la Cruz)
http://www.derwanderstab.de (Puerto de la Cruz)
http://www.gregorio-teneriffa.de (Puerto de la Cruz)
http://www.aventura-wandern.de (Puerto de la Cruz)
http://www.heidis-wanderclub.de (Puerto de la Cruz)
http://www.teneriffatouren.com (Puerto de la Cruz)
http://www.wandern-auf-teneriffa.com (Puerto de la Cruz)
Frank's Wandern 676 363 582 (Puerto de la Cruz)
Wandern mit Alexander und Katja - romahn.tenerife@gmail.com (Santa Ursula, not far from Puerto de la Cruz!)
http://www.teneriffatouren.com (Los Realejos, not far from...you guessed it... Puerto de la Cruz!)
http://www.wanderungen-teneriffa.de
http://www.hans-wanderclub.com (based in Santiago del Teide)
http://www.wanderjule.com (based in el Medano)
http://www.cyberhiker.co.uk (based in Los Christianos)
http://www.tenerifehiking.com (based in Los Christianos)
http://www.teneriffa-wandern.com (an info site in german but with route maps + photos)
http://pateandotenerife.com (pateando tenerife - mucho información - español)
http://www.pateatusmontes.com/ ("senderismo y adventura", La Orotava)
http://www.rutasdetenerife.com (información sobre rutas en Tenerife y foro)