As mentioned before, what will work depends on the signal strength of your stations of interest. What has worked for one person will not necessarily work for another person.
The OP is going to split the signal three times. That means a real world signal loss of around 6 dB for each split plus the loss of the coaxial cable, not necessarily a small amount of signal loss. It is about the amount of signal gained by using a moderate sized directional FM broadcast band antenna.
That is not to say that the signals that he may want to receive will not be strong enough. This is not known at this time. They may or may not be.
Proper grounding for the antenna is very important. It should be to NEC specifications at a minimum. Some locations have additional requirements. In general nothing will protect against a direct lightning strike, but one can go above and beyond the NEC minimum for protection from lightning induced surges.
To increase the gain of an antenna by only three dB, requires doubling the size of the antenna. In the mid-west, snow and ice storms can produce wind loading that requires a fairly substantial antenna support for a larger antenna.
Depending on the available signal strength, a smaller antenna used with a quality, low noise figure amplifier may not be a bad choice. It is not uncommon for some to recommend using a TV type amplifier/amplified splitter. This is case where definitely not all are created equal for a number of technical reasons.
A simple test.
Tape a basic FM dipole antenna to a wooden broom handle and mount it temporarily to the antenna mast keeping in mind that a dipole antenna is the most sensitive to signals that arrive broadside to the antenna. Use this to gauge the local signal strength of the stations of interest. The antenna can be turned to cover all of the stations of interest.
A quality omni-directional FM antenna will provide about the amount of signal as the basic dipole antenna, plus or minus a little. A moderate sized directional FM antenna will provide about 5 or 6 dB more signal for the stations that it is pointed at. If that is not enough additional signal, then a quality, low noise figure amplifier/splitter may be indicated.
For weak signal reception the best location for the FM amplifier is at the antenna. The power for the amplifier can be supplied by the same coaxial cable that carries the FM signal.
Again, making recommendations is at best just guess work without knowing the actual FM signal strength of the stations of interest at the antenna.
One recommendation that is not based on guess work is to use the best, lowest loss coaxial cable that you can.