Urgent how do I know what Ethernet cable I need to buy?

All Ethernet jacks take the same plug: it looks like an oversized landline phone plug.

Get an Ethernet cable long enough to reach from the wall jack to your desk. It will be marked "Cat 6", "Cat 5", or "Cat 5e"; doesn't matter which you get.

If they have "straight" cables, vs. "crossover", get a "straight" cable.

Get a color you like. :-)

Any Cat5e or Cat6 cable will do. Both are rated to full gigabit speeds (1Gbps) up to 100M (over 300 feet). Just get a reasonable length, like 25 feet, and just leave the excess coiled up behind your desk. If you know the size of your room, and where the Ethernet port is, you may get away with a shorter cable, like 10 or 15 feet.

Many colleges monitor their networks carefully, and can detect add-on devices like routers, which they can disable use of. If you want to "modify" what the college gives you for networking, talk to their IT department first. Most colleges hate student run wifi, as it creates a security hole in their networks (they have no control over it). Also, many students run their wifi open, allowing non-college people to connect to it and use the college network for illegal purposes. Remember, the college is legally responsible on how their network is used, and they cannot risk being blacklisted because some student is downloading movies with torrents... Nor can the college afford the time and effort to track down someone who connects to an open (student) wifi to download child porn.
It all boils down to who owns the network and what their rules are. A wired connection for students allows the college to track usage and block unwanted sites.

Get a Cat6 Cable and you'll be fine. Or buy a cheap USB wifi adaptor.

Cat 6 is overkill, it is generally for 10G connections. Most likely the most your dorm will have is 1G or 100M. Cat 5e is probably what you want, (cat 5 is 100M max).

standard ethernet cable is RJ 45 , see the product specification before buying.

When we say "Ethernet" we are talking about standardized plugs, so your only choices are things like the quality of the cable. A "cat 5" (or category 5) cable is good for lower speeds. If you have a 100 Mb or 1 Gb Ethernet backbone to your college room, you want Cat 6 - and your student handbook might even address the requirement. If not, ask the "room mother" to find out if there is a requirement.

Before you ask, "Cat 4" and older cables haven't been used for over two decades. Maybe approaching three decades by now. So either cat 5 or cat 6 will do. Here's another thought: Frequent, the student bookstore will sell books and accessories and will know what is required for the rooms.

As to length, two commonly used sizes are 6 feet and 25 feet. I have not often seen other lengths. You want a cable long enough to reach from the work space to the plug. Beyond that, too much length will actually slow down your response. (It's called an "LC" delay.)

A standard Ethernet will work on everything. However, you want to make sure it has a good enough length or you'll be crammed up against your modem.