I'm looking for a front and rear chainring for my 2009 Bianchi Pista. I measured between the bolt holes and got 3 inches. I converted it to mm and got 76.2. This handy diagram (https://www.hostelshoppe.com/tech_bol...e_diameter.php) helped me see that I need a chainring with a 130 BCD. Is this correct?

Correct. Assuming this is a single speed you want a new chainring (front) and cog (rear).

Do I need to do more math to find the right cog or all they all a standard size? I found a chainring online and I was thinking about purchasing it. https://www.ebay.com/itm/48-TOOTH-TRA...item562b31aec0

If you visit a brick & mortar shop they will help you.

You can get any brand as long is 130 bcd, road chainrings will work just fine also. Dont worry, it will work fine with road chainrings.

Nope. The Pista is a fixie and it won't "work fine" with road chainrings. These are intended to aid shifting and will have an tendency to spill the chain. A track or "flat" old style chainring will be more suitable. Surly sells stainless steel flat chainrings in 130 mm BCD from 38 to 50T that would work better than any chainring intended for a double or triple chainring crank. Look here:

https://surlybikes.com/parts/stainless_steel_chainrings

QBP/Surly stainless steel chainrings were made for single ring setups.
though if you go Wabac, before index shifting took over derailleurs,
and people had to use a skill, to shift efficiently,
The teeth are tall and ramp and pin-less..