In an ideal world you should not need to trim the pot bottom. However, I throw a porcelain clay that loves to crack if not trimmed. Without trimming, I loose 50% due to S cracking on the base in the kiln. The crack does not show up until bisque firing. I found trimming helps compress the base.
The base of the outer wall is pre-trimmed immediately after throwing. I use the round end "(" of my throwing stick to compress the base of the outer wall and cut a new groove at the base for the cutoff string. The "(" compression helps define the area to trim after the pots become leather hard. It also provides a place to use the index finger and thumb of both hands for pickup after pot is cut from bat.
The laser throwing gauge (described in Laser Tech subpage) helps center the piece. Adjust laser to shine on bottom of pot. Hand rotate wheel and move pot by hand until beam equal distance from edge of pot. The beam may need to be moved closer to edge of pot bottom to fine tune centering. For me it is faster than tap centering because I can usually center with a couple of hand rotations of wheel.
Tools
A no clay lug trim bat was made by hot gluing metal strapping to a hardboard bat to form a Y. A piece of rubber shelf liner cut to about the size of the pot is placed on the trim bat. Magnets with 16 lb hold are used to hold piece in place. Cork knobs have been attached to magnets and rubber rings made with foam pipe insulation added to provide additional holding. Always hold down piece with free hand when trimming. A 13 inch bat is used to trim most work and the 14 inch bat is used for plates and extra large pieces.
Ideas and Hacks
Use the laser throwing gauge to center the pot on the trim bat then add magnets.
Start bottom trim by trimming a small center divot for your finger to hold down the piece when trimming.
If trim tool causes chatter marks slow wheel or keep the chatter as a unique feature of the pot.
Not all pots should have a trimmed foot but a foot will improve your hold when dipping in glaze.
If kaolin has lava contaminant and feels rough when throwing burnish the pottery using a stainless steel spoon and spatula made of metal strapping.
The length of the handle should be the same as the height of the mug.
A toothbrush makes a great scoring tool for making slip connections. Just dip brush in water and scrub a small area where you want to attach the handle.
A funnel shaped object or plastic pot makes a tool return the pot back to round. My favorite funnel shape is a 4 to 2 reducer adapter for a shop dust collector.
Use a trim tool made with 3/4 inch wide metal strapping. The trim tool is patterned after a one seen on a Greg Crowe trimming Youtube video. It is shaped like a Y shaped P. Initially it works best when clay is leather hard, not so well when soft or dry. Sharpening the cutting edges with a sanding drum and grinding wheel has helped improve cutting of soft and dry clay. The more I use the Crowe tool the more I like it for all my trimming. It has become my trim tool of choice.