Analog Devices make a couple of LVDT interface chips (AD598, 698), they have good design information in the data sheets. Filtering is discussed in the notes. I have used one of the chips in an LVDT system quite successfully. You could design your own, but then you will need to characterize it, which ADI have already done for you.The band width may be limited by the application, you don't say what the mechanical system on the LVDT is.
You need to establish that first, since it determines things like the required bandwidth, dynamic range, signal to noise,etc., and antialiasing filter requirements.Start with a conceptual block diagram of the whole system, then fill it out with more specific details. The transducer front end will be followed by both analogue (4-20mA) and digital (RS485). The current loop will require appropriate level shifting from the front end device. The RS485 implies digital output, so you will have an ADC as well, so a micro is likely to be needed.Try a book like "the art of electronics", the 3rd edition is most up to date. There is also an extraordinary amount of information on the web. Chip manufacturers often have detailed design notes.Without more details hard to know what else to say, except that there are many ways of approaching a problem, in the end it is usually experience which gets you on the right track in the shortest time. Not having that, if you can modularize the system before you commit yourself to a final design, it is possible to optimize each part of it, swapping out or working on those which don't meet the specs. So breadboard each section until you get it right. Do your maths, essential to meet the design specs, and field test it as well,cheers,Richard