That BF-F8HP is a ham radio and as you mentioned using it on GMRS would make the FCC very sad. A 'real' GMRS radio is not only FCC "approved" but is also MUCH more simple/easy to use. Which GMRS radio is best for you depends on your specific wants, needs, and desires. But a few to consider would be a Wouxun KG-805G (very simple/easy to use), or something like a KG-935G, or KG-S88G which is also waterproof.
If you want something less expensive, I like the Baofeng UV-9G which is not very expensive and is also waterproof..
If you search the Youtubes you will find many reviews and much infos for all of those radios, and many others.
And oh, that Nagoya NA-771 is not made for GMRS and will not perform very well.. If you get a GMRS radio, the stock antennas work great and putting the NA-771 would likely reduce your range. You want the NA-771G which is made for/tuned for GMRS.