I am not sure about the nature of roblox however what you describe here is called web-crawling, thus in order to accomplish this, there is not a single language, most of them are suitable. what I would do first is check weather roblox provides any usable APIs which are there to help developers such as your self in fetching the data you need, in a more use friendly way such as JSON which you can easily use in any language.
for sake of simplicity, since you mentioned that your final result is to make a webserver which serves the data I would go the following way:
Since you already are in a webserver (lemp/lamp) you are in fact already able to preasent a webpage to your devices online. so simpley do step 2, save to the database(mysql) and generate a page matching your need. Note php runs only when the user loads the page on which it resides, therefore if you need periodic checks, just use cron jobs to schedule tasks at certain times and re run your php scripts.
Note 1: the steps above are very general since you did not specify your background in this field.
These steps simply describe how web crawling works in general.
Note 2: If you wish to make your service accesible outside of your network, In order to do that you should configure(usually is the default) your webserver(lemp/lamp) at port 80 and then you should provide your users with your outside ip address.
If your ip is dynamically changing you can use free services such as NO-IP or maybe this.
there are other more complex solutions such as renting a domain name.