There can be a lot of trial and error, and your situation is worse than mine. I'm near the top of a hill going down to the Brazos and can see into South College Station and Snook. I get 1 to no bars in the house with no help, but since I have line of sight to towers I can get full bars with 15dbi gain antennas pointed right at the tower.
Your best bet may be to get a booster. I'd do a kit like this...
https://www.amazon.com/dp/B00RHMFQTOThat should bring your cell phone coverage to good in the house. You could then put a 4G LTE modem next to the indoor antenna to supply internet to the house. The problem with a booster is that it limits you to one signal in one signal out so you can't take advantage of the new MIMO (multiple in multiple out) technologies in modems. Speeds can still be up to 50 or maybe 60Mbps if you can get a full boosted signal. It will really depend on the quality of the signal you are boosting.
The other option is to try just antennas to take advantage of the MIMO technology. This can get you over 100Mbps if the tower can support it and if you can get a good enough signal. In your situation I don't think that is likely.
I have a feeling the booster method is your best bet, but it would take trial and error. I have some antennas and modems from my trials and errors that I should be selling that I wouldn't mind you trying if you are in the area.
Do read through that thread if you have time. There are a lot of different situations and stories told in there, and will give you a grasp of what you are getting into.