I’m looking for the best quality and price on a 13X40 or a14X40 gear head metal lathe?

The basic, time tested, bottom line, rule is — you get what you pay for.
A cheap lathe or a cheap hammer is — cheap. As with anything, reliability and precision is what you want. The more bells and whistles involved, then the more precision in the working parts is required. Reliability and precision takes skiill and workmanship to produce. Exterior appareance i.e. machining/finish is an indicator of the interior milling, machining, and precision the manufacturer requires for its products. You have to decide how much of those things are you willing to sacrifice for a lower cost?

You should consider built in safety features like the safety clutch in the apron that kicks out the feed and the feed/threading safety interlock eliminating the simultaneous engagement of the feed and threading motion. Other things to look for are lathes with a cross ribbed headstock for added strength and stability. Anti-friction mounted shafts and dynamically balanced components. Hardened and ground alloy steel gears, shafts and splines. Oversized precision chrome alloy spindle with a big 2-1/4″ thru hole that is mounted in double row angular contact thrust bearings and 2 double row roller bearings.

Look for swing over the cross slide, and swing in the gap. Hardened and precision ground bed ways on a heavy one-piece close grain cast bed that is fully ribbed for maximum stability and even thermal expansion. Quick-change gearbox for cutting Metric, Module and Diametral Pitch threads as well as standard American threads.

Should have high speed for efficient machining, and plenty of power for heavy roughing cuts. Is the headstock dynamically balanced?

Pay attention to the direct-reading micrometer dials. Is there play? Easy to read?

What equipment do you get or is available? Such as:
Back plate, like 5 7/8″ dia, D1-4
Inch leadscrew
Instruction/maintenance manual
Table chip pan
Thread dial indicator
Tool kit
Set of metric change gears
Two #3 MT hardened centers
Feed rod and double-wall apron
Six position turret
Follower rest
Steady rest
Handwheel 5-C collet attachment
Handlever 5-C collet attachment
Metal cabinet with tray top
Micrometer carriage stop
Milling attachment (inch)
Four-position carriage stop
Set of 15 5-C collet for 1/16″ to 1″ in sixteenths
Telescopic taper attachment
6″ 3-jaw universal chuck
8″ 4-jaw universal chuck
Six position bed turret
10″ Face plate
Round tool post
4-way tool post
1/2″ drill chuck
Live center
Digital readout
Quick change tool post with holders
Coolant tank and pump
Special electrics