You definitely need to amplify your signal to make it stronger. The difference between a distribution amplifier and a preamplifier is that preamplifier is a 2 part unit with the amplifier mounted at the antenna and the power supply mounted in the house. The preamplifier is used to overcome long downlead cable lengths (losses) between the antenna and your TV set or splitter system.
If you have a good signal at the splitter but not after splitting then you can use a distribution amplifier at this point to build up the signal so that you will have enough signals to overcome splitter loss and cable loss from that point. Winegard’s distribution amplifiers would be the model HDA-100 15dB gain or the HDA-200 24 dB gain.Winegard’s most popular preamplifier is the AP-8700. The TV signal is not affected any differently whether you use preamplifier or a distribution amplifier. Just remember that we have to have a good signal strength at the point of amplification.
In your case you have -3.5dB loss at the first splitter and -8.0dB loss for the 4 way splitter so that give you a total splitter loss of 11.5 dB and your 30 feet of cable loss. I would suggest that you use a HDA-100 distribution amplifier ahead of your splitters.