loose well drained mix is a must.

5 parts of screened pine bark fines (usually found in landscaper mix or conditioner soil mix bags).

1 part peat moss (Pro Mix from home depot is a good one)

Controlled release fertilizer like Dynamite is a must.

Add dolomitic lime if needed. If your tap water contains a lot of calcium, use less dolomitic lime or none at all.

I don't understand your question about size. Do you mean you have trees that is 1-2" caliper trunk or wanting to grow them to that size?

By size I mean how big of bare-root trees should I buy? Should I order 1-2' or 2-3'? And what size pots would I need for these size trees? 5 gallon bucket?

Whatever you can afford. at least 3g container is fine. 5g container can get pricey. Look for Sunleaves grow bag online. A lot cheaper than sturdy plastic container if you want to go with that.

Be forwarned! We have had countless posts in past years of high mortality for plants held in long term cold storage. Evergreens in particular can go downhill. Their foliage and buds deteriorate. For us, the bareroot season is finished and forgot about. Please don't say your trees are coming from Tennessee.