You may want to check the price of a radiator (plus shipping) from your local parts store or a place like Rockauto.com. You may be able to get a brand new radiator for around the $50 you're willing to spend. It will be very difficult to get your current radiator dry and clean enough to get some sort of adhesive to stick well enough to seal the small crack that experiences quite a temperature differential. You'd almost need to drain the radiator to atleast below the level of the crack, grind a channel/chamfer in to the crack, clean thoroughly with IPA, then seal and allow the adhesive to fully cure.
The fins of the radiator are made from aluminum, not stainless, and aluminum will corrode. I'm not seeing a hole through the coolant carrying tube in the photo, but it's not a real close up either. If there really is a hole in the tube, since that's the bottom of the radiator maybe that tube is mostly plugged with debris. Considering the radiator hose appears to be original, there's a good chance the insides of that radiator has corrosion and possibly enough debris to seal one or more of the cross tubes.
-Rod