Owner's Manual recommends Pro Honda HP Chain Lube or would you recommend another brand? And why?
Of course Honda will recommend their own chain lube. I have used various brands over the years; whatever has been available really. Having started motorcycling before aerosol chain lube came on to the market, to me they are all good.
No doubt some brands are better than others, but performance could differ with conditions (ambient temperature, rain etc). Probably better to ask locally rather than globally.
They are all better than ordinary oil. That is is better than nothing, but is messy and does not stay on for long.
Country lad that I am, I have used chainsaw chain-bar oil when motorcycle chain lube was not available. It is sticky, and better than ordinary oil too.
As CBR Downunder says,
make sure you use o-ring lube on your CBR250R chain. Solvents used to carry lube in non compatible products can damage the o-rings on the chain.
You should spray the lube on, then leave it for about 20 minutes before riding. That allows time for the solvents to evaporate, and the lube to adhere to the chain. It is a good idea to do it at the end of a ride, while the chain is warm.