Which FICC trading desks to choose?

I will do my best to give you an overview of the various desks you have mentioned.  I think its best to put them into 2 categories. 

Desks where you don't need customers- The market is liquid enough and there is enough volume for you to get in an out of positions using needing a customer on the other side of the trades.  Does not mean you won't trade with customers (you are in liquidity providing business) and won't have to build relationships with them but there is a very active broker screen in these products.  Most of the money in these products in made on carry, and less on bid/offer  

1. Rates: Ton of liquidity in both swaps and cash treasuries.  This is the ultimate macro product as their is theoretically no credit risk.  Very fast paced desk.          
2. Agency MBS:  Based on your interests I would go here, its very macro driven (fed, overall rate levels drive a lot of activity) but also has a lot of nuisances (pre-payment speeds, rolls, coupon swaps, basis risk).  Modeling this stuff is so hard and all the PHDs in the world can't seem to be consistently right.  You don't have to be a PHD to trade it but you are going to be looking at a ton of data and figuring out how to interpret it.  A little more bid ask than rates and more market players to drive flows and ideas relative to rates.  Understanding what the customers are doing and why becomes more important here.  Very fast paced desk.  

3. FX and sovereign debt- Don't know enough about to comment but I would imagine pretty liquid and macro driven as well

Desks where you need customers- Wider bid offer desks that don't have as much liquidity, does not mean you can't prop trade but giving up some bid/offer to the street hurts as you can't do as much size and as such your carry is lower.  Customer relationships and getting focus of your salespeople on your axes is more important.   

1. Agency CMOs: Similar macro characteristics as Agency MBS but with a wider bid/offer and some interesting structuring opportunities.  Very much a customer driven market as you are trying to create custom bonds (duration, dollar price, etc.) that can't be created in MBS.  You will spend a lot of time thinking about relative value between the bonds you are making and other similar assets.  This is a deal desk as a lot of the focus is on creating new bonds and selling them, there is secondary trading but its not as much as the wider bid asks means more buy and hold accounts are focused here.    

2. Non-Agency RMBS:  Also pretty macro, varies by product type but anything without explicit structural pre-pay protection you are going to be thinking about how rates are going to effect pre-payment on bonds.  The further down in credit the more you are going to actually dive deep on the underlying loans but at the stop of the capital stack its more about rel val assessments that you are making vs other similar bonds.  Not as much of a deal desk as all the deals in this space are done off the syndicate desk but you are going to have to know what is going on in your space.  

3. CMBS/CLOs/ABS-  I'd say the least macro on the list especially as you go down in credit.  Also some interesting structural opportunities to think about.  If you are trading BB CLOs/CMBS/ABS you are going to know everything about all the loans in that deal, as you move up the capital structure it becomes more about relative value across asset classes and how the structures work.   

4. Muni Credit- This is going to be most like corp credit, but with a wider bid/offer and lower liquidity.  There is going to be some other stuff you think about besides credit (coupon, call structure, rel val stuff) but you are going to be doing the credit work on these names. 

In terms of who gets paid:  That is way too hard to figure out and literally changes from one bank to the next and at a given bank can change from year to year based on the market environment and whims of management.  The best way to guess is to figure out what the guy running the floor used to sell or trade as people tend to take care of their own.  Focus on picking a group of people you like, a product you think is interesting and a desk with a pace and workflow that works best for you.