A Raspberry Pi 3 in the lab is probably the best way to go right now, as it even has builtin Bluetooth for listening to the tags.
For a relatively simple setup you can take a look at this post about the RuuviCollector, that setup can be entirely run on a single RPi, or it can be “split” so that the RPi only runs the collector and collects the measurements from the RuuviTags and sends them off to another server depending on your needs. Here is an example of the above setup in AWS. My own setup is similar to that, with the difference that I run mine on my own server rather than AWS.
For remote access, a “split setup” is probably the only way to go, depending on the network setup at your lab, it may not be possible to access the RPi “directly remotely”. That is unless your university/lab network has a VPN of some sort that you can connect to remotely and access networked devices from there, or some other solution available.
If you instead want to code your own setup to collect and process data, the ruuvitag_sensor Python package is a good place to start.