There are a lot of questions I have for you, but I can give you some ideas. Here are a few of my questions for you:
1) Why design your own ACDC supply, unless you just want to learn? Learning is great, but you can buy ACDC supplies that do everything you want for very very cheap.
2) What battery chemistry, or does it matter? I would recommend staying away from LiPOs unless you want to use a coulomb counter and keep track of the charge. I'm assuming you don't. Other chemistries are more forgiving, like NiMH or NiCds.
3) What is the output voltage of your ACDC?
In general, to have better conversion efficiency, you'll want to use a switching regulator vs. a linear regulator. You can get around 90% efficiency pretty easily. If this is a one-off, you can use a demo board. If not, you can get modules with integrated switches and caps, or controllers which you would also select your choice of FETs and passives to tune it to your application. LTSpice is what I use to simulate before I lay out a board, and it works great for this.
In terms of handling all the power sources (battery, acdc), you'll want to "or" your power sources using a diode for each different supply. You would want the ACDC to dominate, so you would perhaps set it to put out 12V. In an "or"-ing situation, if your battery was 8.4V, the ACDC would win out since it has a higher voltage. Nothing would be drawn from your battery when the ACDC was on.
However, depending on your current draw, you might not want to use a diode. I know that Linear Technology provides a part for this type of situation called an Ideal Diode Controller. Basically, you use a FET's body diode for the "or"-ing diode, but then you hook up one of their ICs to the gate of the FET so that it operates with only a 25mV drop instead of a 700mV drop. I've used these to push 10A through a diode, and under a thermal camera you could barely tell that the device was getting warm. Beautiful concept, and works great.
If you decide you want to go all-in and know the capacity of your battery, TI makes a chip I have used and would personally recommend with part number BQ2060A. It uses a sense resistor and A/D converter to monitor current in and out of the device, using voltage trigger points to make sure that its capacity readings make sense over time. You will need an I2C bus to read data out of it, so it won't be trivial to implement it.
The output of your battery and the ACDC, after the diode "or"-ing, would go into a switching regulator (for maximum efficiency), or a linear regulator. The output of your switching regulator can sometimes be fed into your linear regulator if you want to have a super-clean supply. Give your linear regulators about 1.5V - 2V above the output voltage that you need from them and you'll get 60-120dB of power supply noise rejection. Also, you can add ferrites on the input and output of your linear regulator and get rid of most the switching noise transients. Google "Jim Williams" and "ferrites" and you'll probably come up with one of his application notes that describes this.