Properties of root raised cosine filter
Your bipolar sequence at one sample per symbol is equivalent to a perfectly synchronized sequence of symbols with no intersymbol interference (ISI). Intersymbol interference in this context refers to the tendency for symbols that precede and follow the current symbol to interfere at the receiver. That is, at the correct sampling instant for symbol $N$, the receiver also sees some of symbols $N-1$ and $N+1$ (and possibly more in each direction) mixed in. This causes an increase in symbol error rate.

In general, ISI is caused by some non-ideal channel impulse response between your transmitter and receiver. This can be caused by several phenomena, including:


A multipath communications channel (e.g. a wireless channel). In this case, the receiver observes a signal that can be modeled as your originally transmitted signal convolved with some impulse response.
The use of a non-ideal pulse shape. On the AWGN channel, the optimum receiver consists of a filter whose impulse response is matched to the transmitted pulse shape. The receiver therefore observes a stream of pulses where each has the shape of the originally transmitted pulse shape convolved with itself. The choice of the pulse shape is important to ensure that the receiver doesn't encounter any ISI after applying the matched filter.


This is why the root-raised cosine filter is often used. When convolved with itself, the result is a raised-cosine response, which has zero ISI (it is exactly zero for all multiples of the symbol period $T$, apart from $t=0$). 

With that said, there are some practical considerations when designing your pulse shape. When you actually transmit it, you'll need to oversample it in order to meet the sampling theorem's reconstruction requirements. A typical oversampling rate might be 4. 

The rolloff factor controls how much bandwidth the RRC-shaped signal will occupy. In general, the more excess bandwidth, the better you can expect your synchronization algorithm to perform (i.e. you would usually observe smaller error from your timing recovery subsystem with a larger rolloff factor). However, this comes at a cost of more bandwidth required to carry the signal.