A dedicated DAQ device is the best tool for this job.
An scope shines in much other areas compared with a DAQ card, but it is not the best tool for data acquisition experiments.
A DAQ card will be much more flexible to program and integrate in a experiment system. It allows continuous data acquisition, and much better resolution. An scope, if I'm not wrong, is limited to 8 bits only. DAQ cards can be found with 12, 14, 18 bits.
Maybe an scope is sufficient for this experiment, but can limit future ones.
A high performance DAQ card can be much more expensive than an scope, but there are various options that may be good for your needs and not break the bank.
A established brand in this field is National Instruments. If you have no objection, maybe you can find good used options on ebay.