What type of wire should I use for about 80ft run to a She Shed in 1" conduit for a 60 AMP subpanel. Can I use 6-6-6-6 Gray Stranded AL SER Cable?
SER cable is no good underground
NEC 338.12(A) point 2 prohibits the use of type SE (style U or style R, it doesn't matter) cable underground, even when in a conduit/raceway.  Besides, you really don't want to be pulling that alligator of a cable down a 1&quot; conduit to begin with, as it won't fit very well at all, leaving you calling the electrician in to bail you out.  In particular, a typical 6-6-6-6 Al SER cable has an OD of 0.717&quot; or 18.2 mm, which means it takes up 260.5 mm2 of fill area.  This barely fits into 1&quot; conduits of most conduit types, a bad omen for a multiconductor cable to begin with, and does not fit in the worst-case scenario of a 1&quot;, Schedule 80 PVC conduit.
Furthermore, 6AWG Al is limited to 50A when landed on the 75°C capable terminations in distribution equipment, not the 60A you were hoping for.  As a result of all of this, I'd put in 3 6AWG copper THHN/THWN wires instead (two blacks and one white), with a bare 10AWG copper ground wire.  This takes up a mere 103.4 mm2 of fill area, less than half of the space the cable takes up, while being a far easier pull through the conduit, and fully Code-legal in this underground application.
Once you get to the shed....
Once you reach the shed, you'll need to install a subpanel there.  This is where most folks screw up; they chintz out and put in a tiny panel, thinking that's all their feeder can support or simply looking to shave a few bucks off the project cost, when they're really setting themselves up for an expensive panel swap down the road.  Instead, I'd put in a 24-space or 30-space, 100 or 125A, main breaker panel.  The oversized main breaker in the subpanel is no big deal as it's simply serving as the shutoff switch required for the structure by NEC 225.31, and the extra spaces provide plenty of expansion room for whatever crazy tools your significant other decides to get into.
Because you're putting in a feeder and subpanel, you'll also need to run some 8AWG or 6AWG bare copper from that subpanel to a pair of 8' ground rods driven a minimum of 6-8' apart.  This provides natural electricity, such as lightning-induced voltages, a path back to Mother Nature, while the equipment grounding wire in the feeder provides an easy route wayward utility-generated electricity can take to get back to the neutral-ground bond in your main panel and thus back to your utility.  As a result of this, you'll need to make sure the bonding screw or strap in your new subpanel is removed, or simply left uninstalled to begin with, when you install it.
TORQUE ALL LUGS TO SPEC
Last but not least, 2017 NEC 110.14(D) requires that all breaker and loadcenter/panel lug-type connections be torqued to the labeled torque values using an inch-pound torque wrench or torque screwdriver.  Even if your jurisidiction hasn't adopted the 2017 NEC, this is still a good idea anyway, as this Code change was made because of studies that were done that showed that the electrician's office manager (or a DIYer) was as equally unlikely to torque a connection correctly with regular hand tools as the electrician was!