In frum circles, until five or ten years ago, I’d say at least 90% of all men brought their tallit and tefillin to weekday Shacharit in a regular zippered tallit and tefillin bag cover made of nylon. The idea is that you need something to protect and show off your fine velvet tallit and tefillin bags, and carry them under your arm.
Cheap nylon covers will fall apart after just a few months, whereas quality covers last significantly longer.
At one point mine fell apart and I decided I wasn’t go to buy a new one. I had an unimpressive velvet bag set, priced at around $15, so I didn’t see a need to provide protection, and I felt the plastic detracts aesthetically. I realized that my tallit bag was roomy enough to put the tefillin in, without a tefillin bag at all. (According to halacha, you have to be careful not to grasp your tefillin before your tallit, so I would put the tefillin inside the folded tallit with the fold right next to the zipper, making it impossible to get to the tefillin before removing the tallit.)
My next tallit and tefillin bag set is going to be more expensive, because, well, you get what you pay for. Almost invariably the materials and workmanship on a $30 or $40 set are much higher caliber than with a standard $15 or $20 set (although in some cases you may be paying for for elaborate embroidery design with inferior materials).
Also, attractive tallit and tefillin bag sets lend honor to the mitzvahs of tallis and tefillin, so I’m willing to pay an extra $10 or $20 to honor these cherished mitzvahs.
Tallit and tefillin bag cover with strap
In the last decade someone realized that it’s too much work to carry the nylon bag with tallit and tefillin inside without a carrying handle. So he invented a hybrid bag with a big nylon “window” in front to show off the embroidery. These quickly became popular and today I would say they are essential for just about every bar mitzvah boy. My sons like them not just because the carrying handle and shoulder strap make life much easier, but also because they like all the pockets to stash things in. If you buy one for your son, it’s a good time to teach him the enormous importance of learning to turn off the ringer on his cellphone (if he has one) before going into shul or yeshiva. These bags come in three sizes: small for just tefillin, medium for tallit and tefillin and large for those who have two sets of tefillin (Rashi and Rabbeinu Tam).
I have seen that some tallit shops in Jerusalem are starting to introduce the idea of a regular bag with no “window,” and I predict this will eventually gain some popularity.
Another option is Tfidanit tefillin carrier. These are very popular among soldiers and commuters who need sturdy, dependable protection for their tefillin. It also has a tefillin bag cover that wraps around the tefillin carrier, and can be attached for single men who don’t wear a tallit. If you are travelling and need real protection for your tefillin, but cannot afford the Tfidanit, you should be able to find a very strong square tupperware piece that can do the job. But be aware that once used for tefillin you cannot later convert it for use for any mundane purpose (unless you stipulate a t’nai) before you start using it for tefillin.
You can find imitation tefillin carriers for much less, but they are vastly inferior to the Tfidanit.