USPS shipping - First Class and Priority
First Class mail - 3-5 days on average, no guarantee (think 4-5 traveling from the East to the West coast or vice versa). Parcel must be under 13 ounces, anything over 13 ounces has to go Priority mail (if shipping by air). Price will vary between $1.95 - $3.65 standard retail, add $.85 if adding delivery confirmation (tracking). Prices are slightly cheaper if done online with commercial based pricing.
Priority mail - 2-4 days on average, no guarantee (I'd say 2-3 going to a major city, 1 day going to a city/state near you, 3-4 going across the nation). Anything over 13 ounces has to go Priority mail, but anything UNDER 13 ounces can also go Priority too. Priority mail is slightly faster than First Class mail. Priority prices start at...
***Flat Rate
$5.15 Priority Flat Rate envelope
$5.30 Priority Padded or Legal Size Flat Rate envelope
$5.35 Small Flat Rate box
$11.35 Medium Flat Rate box
$15.45 Large Flat Rate box
***By Weight (in a Priority Mailing box or your own box)
$6.30 0.1-1.0 pounds
$10.40 1.1-2.0 pounds
$13.85 2.1-3.0 pounds
$16.70 3.1-4.0 pounds
etc, etc
Delivery confirmation for Priority is $.75 retail or free if done online.
Because plants are pretty light I'd say in most cases you're probably sending out small First Class parcels or any of the Flat Rate envelopes and small box. You can get all the supplies for free at your local PO, or you can just order them for free online at USPS.com. Everything is free, including shipping. I recommend ordering online because they have a much better selection of free mailing boxes (remember, by weight) that come in a variety of sizes.
Let me know if you have more questions, as while I do not mail much stuff out myself I do conveniently work at a Post Office so all of these things are deeply embedded in my quickly-going-postal brain. I didn't include any sort of run down on Express mail as that'd never really be used for plants, but if you're curious about that class of mailing just let me know.