I think you'll find if you read the book or on the site, or take a consensus that they would say to start with copaxone. Do your homework and read articles and do even read the info from the drug companies. What I can tell you is:
do not think that one needle is easier than 3 or that 3 are easier than 7.
Here's how it works:
Avonex is 1x weekly. It sounds easy, but you will literally lose a day of your week suffering. It does get better with time, so that would not be permanent. Also, the needle looks like a nail and you have insert deeply into muscle without an auto-injector
Betaferon is every other day and is a shorter needle. You may have itchy bumps, and you will also have those horrible feelings on shot day. However, they say they're not as bad as with Avonex.
Copaxone is daily, has the smallest needle and has few side effects, if any. It's also been proven as effective as Betaferon and more effective than Avonex. What's more, you have no risk of damaging your thyroid or liver and don't need regular blood tests.
I'm on Avonex. tomorrow is shot day, so i don't really plan anything special. Just getting through the day is my goal. My white blood cell count is lower than normal (it lowers your immune system) and I now get colds whereas I never used to. I also can't be sure that my reduced immune system will not let in some cancer or fungus or something else. Betaferon has the same trouble.
Now I know several people who are doing fine on avonex after 10 years. I'm doing well to, being on the diet meds, exercise and meditation. You should do all of them and not count doing any singe one as doing as enough.
Don't let the number of shots alter your decision too much. I imagine that 1xHuge side effects or 3.5xmild side effects or 7xalmost no side effects are all the same. So do the math some other way. Of course, if you travel a lot and carrying 14 packs of refrigerated medicine is difficult, or you're an archeologist and need to go out into the jungle for days at a time, then the Avonex might be a good choice.
I hope this helps.