"Our home’s basement needs some tuckpointing/repointing and perhaps some drainage due to water intrusion. I’m curious if you have recommendations?"
The only real way to truly correct water intrusion in a basement is to trench around the exterior of the basement walls and lay drain tiles/perforated PVC, a layer of gravel, and then to close it back up. The water infiltration is likely the cause of the need for tuck pointing on those basement walls.
Things to check -
Are the walls cinder block? Rubble stone?
Are the downspouts running far enough away from the house?
Is the terrain around the house sloped away from the house enough to get run-off as far away from the house as possible?
There are some inside “bandaids” that are marketed but they are just that, a bandaid. The water is at the interior surface of the walls with any of those solutions.
If you can get a French drain on the outside, tar/seal the exterior wall and fill with gravel and then topsoil, you will most likely solve your problem. Remember to grade the soil away from the house a bit.
If that doesn’t resolve the problem, you can always go back at a later time and install a drain and sump under the basement floor. One is not dependant on the other. Just be sure the perimeter drain around the exterior has a place to dump the water.
If the face of the brick has burst off, that is the result of water penetration. In the winter, that moisture freezes and expands causing the brick face to burst off. The source of the water penetration must be found and corrected. It could be a bad gutter or downspout, a leak in the roof or the lack of a drip edge. Once the source is found and corrected, depending on the amount of damage one of the following options will work: