Without disc brake tabs, you will likely stick with a similar style brake. Tektro brakes I have been involved with were not known as serious stopping power.
Not knowing if you plan to accomplish the task yourself or bring it into the shop, but basically this should help.
For reasonable prices, Avid offers some decent brake systems from their model line of "Single Digit", probably I would consider looking into the SD7 series or better.
Avid also offers the "Speed Dial" series of levers to compliment the actual brake arms. The Speed Dial 7 would be a good choice.
Shimano has also offered some excellent stopping rim brakes. While I don't mind them when new or with low hours of use, the higher end Shimano brakes have multi linkage and can get sloppy with time.
Either setup should be a good improvement, and to take it further, more grippy brake pads can be installed.
The cable routes should be as short as practical with as few bends as possible. The design of your bike might have the rear brake cable route not optimized by the rear seat.
This gives you some options and choices. Possibly for the riding you are doing, you may even find that upgrading the brake pads and optimizing the cable length and routes will be adequate.
Best of luck with it.
PK
