An ideal pilot signal for channel estimation (without any apriori further knowledge of the channel) would transmit power uniformly across the channel and be easy to replicate in the receiver for channel estimation, as channel estimation cannot be determined where no signal exists for comparison, as well as carrier and timing recovery for a synchronous digital modulation data link. PN sequences are good choices due to their characteristics that mimic white noise. Further and due to the same properties resulting in an auto-correlation that appears as a single impulse as expected with white noise, they are also useful for synchronization such as estimating the start of a data packet. The PN sequence also provides fast convergence for timing and carrier recovery in a digital data link, but you may also consider adding a certain duration of a 10101010 sequence after the PN sequence (if the overhead allows) which will provide further robustness for timing recovery.
A chirp could also be used providing both properties of having a white spectrum (on average across the frequency band of interest for which the pulse is applied) and a sharp autocorrelation function (as demonstrated by the matched filter output being a “compressed pulse) although the use of PN codes could more easily offer a greater set of uncorrelated patterns that could be used in the same pilot time interval which could be used for other features related to packet identification (if desired). A chirp does not readily provide for carrier recovery since it is difficult to distinguish carrier offset from time offset, nor does it provide information on the data rate that the toggling of the PN sequence would provide.
The primary use and purpose of a pulse shaping filter is for applications where the spectrum must be contained. (With no pulse shaping filter, and the transmission of rectangular pulses, the ideal matched filter becomes and integrate and dump filter (or equivalent moving average process) and there is no penalty in doing this other than the much wider transmit spectrum. Distortion to pulse shaping is a non-linear distortion mechanism such as driving amplifiers too hard into compression rather than linear distortions such as pass-band ripple, reflections etc that can be corrected for with channel equalization (as these distortions end up being similar to multipath that the channel introduces). The resulting spectrum after a pulse shaping filter is also flatter across a narrower spectrum (just over B wide for a symbol rate of B symbols/sec) while a rectangular pulse will have about a 4 dB roll-off over that same bandwidth. For this reason the use of a pulse shaping filter for channel estimation patterns will result in more efficient channel estimation applying more equal power across the channel. When timing is of primary concern (such as with GPS), pulse shaping will degrade time resolution since for that the widest bandwidth is desired (for the sharpest autocorrelation peak). To create a matched filter, it is typical to decompose the pulse shaping into the cascade of two identical filters (thus square root filters), with one in the transmitter and the other in the receiver.
Here is a link that describes the trade space with pulse shaping further, but again first consider what your spectrum containment needs to be and then design from that; the tighter the pulse shaping the more complicated the receiver will be both with the duration of the matched filter and in the timing recovery algorithm/loop.
Pulse shaping with RRC : Number of taps