Tips on selecting Pistons??

Stock pistons for that LA model 360 will be around .110" in the hole. Typical SCR with a later Standard Felpro head gasket (thicker than the original) and a .030" overbore will be around 7.5:1..... nothing to get excited about and worse at altitude.

To get this number, I used the Pat Kelly calculator (on tab #3) with the following inputs:
Bore 4.030"
Stroke 3.58"
Chamber volume 72 cc
Gasket thickness .051"
Gasket bore 4.17"
Deck clearance .110"
Flat top piston with 9 cc dish volume

Use this calculator or get comfortable with another and learn the common parameters and you can check SCR and DCR over an over to your heart's desire with all sorts of parts choices. This calculator will also figure your DCR with the proper inputs.

For street use, I like to look for SCR over 9:1. This is likely to push you to very different pistons like Speed Pro H116CP (has similar piston and pin weight to the stock so probably no rebalancing of the crank), or KB232's for about 9.5 SCR (same thing on the weight..).

But all this will vary as you change heads and a few other things. Just keep in mind that a good safe region for pump gas is 9.5 SCR max (and low 8's DCR) for iron heads, and a bit more of AL heads.

So what do want in a 'pretty mean' street engine? That can have all sorts of meanings! Glad you are looking at this the right way: picking the application and building to that.