Participating in chess tournament

You do not need to be rated to play in a tournament. Most tournaments offer several categories. For example, the Stockport Rapidplay tournament, has open, major, intermediate and minor. To enter the minor you have to be rated less than 110 (or be unrated). So just find a tournament and start to play. 

30th Stockport Rapidplay, The Davenport Hotel, Buxton Road, Stockport SK2 Contact: Peter Taylor Email: pht@rover12.wanadoo.co.uk - One day 6 Round Swiss event. Four sections: Open, Major (U170), Intermediate (U140), Minor (U110). Each player has 30 minutes for all moves. Prizes: £130, £80, £40 and Grading £40 each section. Stockport League Trophies, Veteran, Junior and Buxton prizes. New large venue close to the M60 motorway

I work at university by the way - I don't know for sure but I would be amazed if your student vias stopped you playing in chess tournaments.

And do you get a rating after playing the tournament?

In Italy if you are regular immigrant (a student visas is enough) you just need to associate in a club as a foreigner player, then to play a omologate tournament and you will immediately get Fide ID, for the Fide rating you need to play 5 games against Fide rated players (in Italy is easy to found what is needed in a normal tournament).

Total cost: Just pay Italian chess federation, the club and the tournament ... with gran total 150 dollars you can Achieve at the performance.