Tascam US1800 interface with external mic pre

You would either use the line input ( channel 11/12)or 13/14)  or even better  buy a pre amp that has SPDIF outputs, better quality ones do.

 You don't run a pre amp into a pre amp, That's a impedance miss match.  Tascam has 8 mike pre amps for use with low impedance mikes and equipment, Then there are the instrument inputs 9/10 for guitars and synths. There are 2 stereo pair line level inputs on the back. 11/12 & 13/14, you use those for line level ( hi Impedance ) sources. 

The Tascam has pretty good mike pre amps so some lower end budget pre amps will not make any difference to your sound quality, some could make it worse. 
I use a Yamaha 01V digital mixer with mine because I want the compressor on my vocals. I don't think the mike pre amps are any better than the Tascams. I have used the Tascam pre amps as well and found absolutely no fault with them. I just have to have the compressor , that's all. If the Tascam had inserts you could do the same but it doesn't. 
So A mike pre amp with inserts and/ or a compressor and SPDIF output would be my only consideration.   

Almost any built-in interface pre is good - as long as you don't push them too hard.  See Sound on Sound's preamp shootout, where they couldn't tell the difference between high and low end pres when recording a Yamaha player piano.
 
However, when you push things stand alone pres, esp. models with transformers and tubes, separate themselves.  Trans and tubes tend to saturate, thickening and making your sound fuzzy before the unit hits saturation.  Most IC pres just go straight to unpleasant distortion.  Saturation helps you, as an engineer, distinguish the sound, esp., say, lead vocal as opposed to backing cowbell.  Which would you prefer your listener to concentrate on, have their ear drawn to since it stands out?  Unless you are Will Ferrell, and I wouldn't wish that on anyone.
 
Get an RND Portico II if you want a great pre and all the other input fixings - it will make your AKGs (and shure 57s) sound their best (and the II pre is different from the portico line of pres).  If you don't have 3 grand a pop, the Warm WA12 is a nice (and cheaper) take on the API 312 pre while the ISA One is a lighter, less thick sounding transformer-based pre.  Both of those can be had for -$400 or so used and can be driven hard without breaking up.  And there are plenty of pres in between those price ranges.