Be very careful about the coverage maps. If they say you are on the edge that most likely means it will only work if you stand on you roof and hold your nose just right.
Even when you are in what is suppose to be strong coverage areas you sometime get no signal. Most the time the fine print on the coverage maps says that this is for outdoor use. Best advise on this is borrow a LTE device from verizon and see how much coverage you get. This will also be useful for placement of any booster since you need to place this device in the strongest signal area. A smart phone tends to be the easiest to do this with since I am going to bet you get the best signal on your roof someplace. Even if verizon charges a small amount to lend you something it is worth it, the amplifiers and antennas needed tend to be very expensive so you need to get it right the first time.
Many of the signal amplifiers will work with all the bands. You need to ask what frequency they run the 3g on. More than likely LTE is running on 700mhz. The amplifier needs to support the other frequency.
Depends where you get the router. Verizon should offer one with ethernet ports. You can always use a USB dongle type device and a third party router that is not locked to verizon.
The best type of device I have seen to do this is a outdoor 3g/4g router. Instead of trying to retransmit cell tower signals it receives them and then sends WiFI out instead. Sorta a 3g/4g hotspot built into a directional cellphone antenna. I have not seen a LTE product yet but I would suspect they make them. Of course this does not work if your plan is to use a cell amplifier to improve your ability to make cellular telephone calls
I'm going to have to use a Verizon device for internet access, as no cable or dsl available in new house. VZ tells me I'm on the edge of 4G coverage. What's the best way to try to get best(fastest, most stable) signal inside the house? Will one of the 4G amplifiers (like Wilson) also prop up the 3G signal, if the 4G drops out?
Also, is there a way to hardwire one computer to the router, vs having all devices connect via wifi. I'm trying to reduce latency as far as possible, at least on one computer.
Thanks for any thoughts.