You have some pretty weak signals. It will be a stretch, but with a lot of hard work and some luck, you *might* get the first 3 channels on your chart. Try entering higher heights to see if it improves your chances.
As for you questions about signal hunting, I used a handheld portable TV with built-in signal-strength diagnostics to do exactly that. Mine is an RCA and the meter is qualitative (poor , fair, good, very good, excellent).
Professional installers use some pretty pricey signal meters that when they “walk the roof” during installs. Rabbit73 might recommend one for you. I built a poor-man’s version for about $70 using a Winegard Sensar Pro Signal Strength Meter unit that is designed for recreational vehicles- RVs. It requires a DC blocker, a hobby enclosure, and an 8-battery power pack to supply 12VDC. See R. Ross’s review on amazon for instructions.
I recommend the RCA handheld because when you’re done using it, you still have a TV. I like to take mine hiking to see how reception is when we get to the top. My wife hates that.
As for distance between house and antenna, 300 feet is not unheard of. My antennas are 55 feet up in a pine tree about 150 feet from my house. You'll likely need an amplifier. KT-200 is one of the best low-noise ones out there. Juice is good too. Depending on the length of your run, you may need a lot of gain. Check the loss vs. distance tables for UHF and VHF, and use a single length of new RG-6 between amp and house. RG-11 is less lossy, but more expensive. I recommend putting the amplifier at the bottom of the tree. See my thread “Reception Help in NH” for pictures and the whole story.