I’m wanting to get a ham radio license and a good base station set up in my home. The reasoning is to communicate to my family approximately 40 miles away from me in case of a emergency or SHTF scenario. What would we both have to have to accomplish this? I am really inexperienced in this field of ham but since this is the reason me and my family both want a setup for both our houses it’s important I know what for us to purchase. Thanks so much! -Casey
With 2 meter FM and common 50 W base or mobile transmitter power and plain vertical quarter wave antenna, range over flat ground to a similar station is roughly twenty-five miles, or forty km (limited mainly by line of sight and horizon scatter). Raising the antenna will increase this, but not dramatically. Repeaters in my area that are roundly 1500 feet (~450 m) above average terrain have only about a forty to fifty mile (65-80 km) range to car-mobile rigs of similar power, and then only without intervening terrain.
What you need with the terrain and tower you describe (assuming the mountain your relatives live at the foot of isn't between the two stations) is a directional antenna. A very modest Yagi at the higher end can give enough gain (both in transmit and receive) to give pretty reliable ground diffraction contact at forty miles (65 km) with fifty watts on 2 meter FM. This makes you independent of repeaters.
Also very important is to ensure that both stations have emergency power -- at the least, a substantial battery backup, kept charged and tested regularly (a single car battery will run a 50 W transceiver, mostly receiving, for a couple days).
For VHF or UHF, your range is mostly going to be limited by terrain, like Zeiss Ikon writes. On flat terrain the radio horizon can be estimated by a simple formula, but that's not of much use if the terrain isn't flat.
So, you can use a tool such as heywhatsthat to see what terrain is visible from where. If you have a clear line of sight over the path between the stations, just about any VHF or UHF radio should do. If you only just barely don't have line-of-sight, you may still be able to communicate with enough power and antenna gain.
A more sophisticated method to predicting propagation is the Longley-Rice model. There used to be some free online tools for this, but they've all gone away.
Alternatively, HF ground wave or NVIS could provide reliable communication at this range regardless of terrain. A 100W transmitter and a simple dipole in a tree would do nicely. You can play with VOACAP to run some specific scenarios.
At 40 miles (65 km), assuming that terrain doesn't get in the way, you have a choice between HF and VHF/UHF. For HF the radios are expensive, maybe \$600 for a good used one, and a simple wire antenna and coax would cost about \$150. Several HF radio models also include VHF/UHF. The antenna could be strung up between two trees. You could talk to half the hams in North America fairly easily, and hams in further places with persistence and skill. Terrain isn't usually an issue, unless you're deep in a valley.
For VHF and UHF, the radios are less expensive; a good used one can be had for \$100–\$200. At 40 miles (65 km) you could talk through a repeater with inexpensive omnidirectional antennas (say $80 for the antenna and coax), or directly through directional antennas mounted up high (20' or 6 m would probably do), which might cost \$120 for antenna and coax. This assumes that the directional antennas are aimed at each other, and that terrain doesn't interfere. If you get directional antennas, you might also want omnidirectional antennas so you can talk to locals in all directions.
The price estimates are for one radio and one antenna, so if you must also pay for the equipment at the other end then double your estimate. Personally I'd budget at least another \$100–\$200 for miscellaneous items such as coaxial connectors, rope, shipping fees, nuts & bolts, etc.
I would echo @ZeissIkon's advice about emergency power: radios are useless without it when the power grid goes down. I'd also suggest joining the local ham community, if for no other reasons than using the radios regularly and learning how to fix common problems.