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Congrats on your internship. Very exciting. I work in NYC, have done sell-side and buyside in mortgage bonds. Couple thoughts. 

1. The desks pick you, so be humble on every desk you work at. First one in, last one out. Trading is stressful, be happy to run around doing errands and making everyone's life easier...coffee, lunch, etc. No job is beneath you, traders/salespeople will recognize that and like it. If you become the designated coffee/lunch person, and tie out everyone's PnL for the day, you will 100% get an offer.

2. Be open to sales. The goal is to get a seat/offer. Once you're on a desk, you can apply to move after a year or two. 

3. I know Citi has a large FX operation however you have to believe that FX will continue to go more and more automation (less headcount). My vote would be bonds. Duration, adjusting hedges is super hard to automate; so bonds would give you a nice career path working at Citi or a HF later. I'm partial to mortgages, they are a fascinating product, a huge market, and modeling prepays ie Human behavior is next to impossible. Second would be government bonds (any tenure will be fun), huge market, global macro is great and always interesting. 

4. Ask questions but do not be annoying. Which desks make the most money, find out and go there? Do you want to make a + on 500mm USD/CAD trade (Forex does not have wide spreads), 4 ticks trading 500mm US10yrs or 20 ticks trading 500mm stripped down GNMA 3.5 floaters?

5. Any structuring is also great. Equity-linked notes, deriv structuring, mtge structuring all good with BIG upside. 

6. If they invite you out, you 100% go. Have 1-3 beers but do not over do it. Show that you can have fun but are not going to be hungover at work. 

Best of luck with your opportunity.