soldering a PCB for the first time questions

I am assembling PCBs for the first time. The components are thru-hole and there is a ground plane that many components are connected to. I had the PCBs made by standard processes at a well-known supplier. Should I be concerned when soldering the pads that do not connect to the ground plane? I am concerned that there could be a short if the solder accidentally attaches to the ground plane when it should not. So far I haven’t had a problem as far as I know, but this is my first PCB design, and first time doing assembly, so I wanted to clarify that. Also, I am using a solder flux pen to wet the connections before soldering, is this a good idea? It seemed to help the flow. I have used 2 solder flux pens. One is “Rosin Flux Pen” by MG Chemicals, RA type, non corrosive. The pen I just started using is “Flux Pen for Rework” by SRA Soldering Products, No. 312 Alcohol-based, No-clean Flux. Are either of these acceptable or good to use? The SRA flux seems to work better and dries less yellowed.

Soldering through hole by hand? Just use rosin-core solder, no need for additional flux.