Range normally from 1 - 5, depending on kind of music played, clarinet players should have a combination of different mouthpiece and reeds.
Jazz clarinetist should use a big tip opening, long facing with soft reeds.
People tend to go higher and higher in strength is simply because stiffer reeds produce a more stable tone in the higher register. I am sure that all of your tutors agree that it is easier to reach a high note on a strength 4 than a strength 2.
Beginners should start soft with open tip mouthpiece while advancing and advance players can try stronger reeds and closer tip mouthpiece.
3 things that will affect the tone of a clarinet is the mouthpiece, the reed and the ligature. (not to mention the clarinet itself, but nothing much you can do about it unless you repad the whole thing with Goretex pads and change to better materials).
If your clarinet is your speaker, then your mouthpiece is your mic, a good speaker with a bad sounding mic will not produce good sound. Personally i would recommend beginners to try on plastic mouthpiece first but plastic mouthpiece not much to control. If they wanna upgrade, go for a hard rubber one. Selmer, Leblanc and Vandoren produce fairly good mouthpieces. I have been using a Vandoren B45 for 6 years but then because I advance until I play a strength 4 now, so have to upgrade to mouthpiece with closer tip. Now I am using a Vandoren M13 lyre mouthpiece, i must say it produce a fairly centred tone.
Personally, if you can afford it, you might wanna try pyne mouthpiece or bay mouthpiece, these are handfinish mouthpiece, they have been extensively tested before sold. Played on one of them before, it sounded so nice and so much easier to play. but the price is double of M13 lyre.
Ligatures, this is important. an ideal ligature can hold the reed in place yet exert the slightest uniform pressure on the reed so that the reed can vibrate freely. You must realise, the reed does not stop vibrating when it reach the mouthpiece. The whole reed vibrates together. Personally, if you want to sound bright, go for a metal mouthpiece but should your metal mouthpiece goes out of shape, then good bye to it, because once it goes out of shape, the slightest screwing will cause the reed to go our of place. Leather mouthpiece are good but then they still do not exert uniform pressure but still good enough for students. Before the invention of ligatures, clarinetist use strings to tie their reeds but it's kind of troublesome. nowadays, the close to ideal mouthpiece, it's fairly simple. According to David Pino - author of The clarinet and clarinet playing, he said velcro is good. one strip tying across is fairly ideal for the mouthpiece. I tried, I think it's rather good. He suggested the ideal method is use flat shoe strings. Have not try that, but will try. You guys might wanna try a pyne clarion handwoven ligature. It is simillar to shoe string method but it's easier to tweak the tone of the reed. Here is a small tweak you can try. For 2 screws ligature or ligature where you can adjust the pressure of the upper and lower part of the ligature, exert more pressure at lower part will produce a darker tone while more pressure on the top will produce a brighter tone.
Reeds, the most important part. if you choose the wrong but functional mouthpiece, you can still make sound, just harder. if you choose the wrong ligature, you just have a different tone. If you choose the wrong reed, you will sound terrible or does not make a sound at all.
Personally, i will not go for neither Rico royal or Vandoren. Simply because out of a box of 10, i can only choose may be 3 if you are lucky that sound good, others need extra work to be done. I had once threw a whole box away because they all sound terrible. Currently, I will only go for either
Gonzalez
http://www.gonzalezreeds.com/index.php?page=eng-home
or Zondas. I am currently trying Rico Reserve, the first one sounded extremely well though, but i do not know the rest.
Back to Gonzalez, the FOF - for our friends reed has a thicker heart which will allow you to produce a fairly darker tone. It sounded so dark when i was play E lucevan le Stelle in Tosca, so nice. You can use the regular cut if you want a brigher sound. The results, I have tried 10 reeds so far, only one of them failed because I accidentally chipped it.
If you want good reeds, play on hand select reeds and one advice, must break in your reeds before you can consistently play on the reed. Do not use one single reed for practice for the whole month, your reed wont last 2 weeks if you play on it everyday for 2 hours.
For information on how to choose reeds and break in correctly, you may want to look at the following site.
http://members.tripod.com/~Jean_Johnson/reeds.html
(Jean Johnson is a professional Clarinetist)
Regarding synthetic reeds, I am not against it. just have not try enough to say anything. So far they can make quite a good tone but adjustments are hard to be done on the reed.
Good luck on playing the clarinet.
Actually the barrel does affect the tone in an indirect way, some barrel's tapering design may affect the ease of blowing, so if you choose the correct barrel, it will enchance your tone.
<Added>Regarding ClariPatch, actually it does work somewhat. But I seldom use since I have found the correct reed to the correct mouthpiece.