If you pick cogs and chainrings that add up to the same number of total teeth, the wheel will move very little in the dropout or track end. (I am assuming you have a bike with either the horizontal rearward opening track end or near horizontal front opening droppout. If this is a derailleur bike with vertical dropouts, you have a much more demanding task that that bike would ve a poor choice for starting out fix gear. Single speed with a rear derailleur or "singulator" to take ou chain slack would work.

Yes, sticking to 60 links (or whatever) works. You still want a little wiggle room to get the chain slack right, but you don't need much.

On my old Mooney, I installed a triple chainring and have three fix gear cogs in back, each of which lines up exactly with its respective chainring. To get true mountain gearing, both uphill and downhill, I can run a 46,42,36 crankset and 13, 17 and 23 cogs (59 being that setup's magic number). (This was not done either easily or cheaply and I had no precedents to work from, But the end result is a blast!)

Ben