First of, figure out what your budget is.
Squier is technically the "budget" line of Fender although a high end Squier VM or CV is equal to, or almost equal to a Fender Made in Mexico (debatable on that

)
In order of quality and relative price for new in progressive order good to best.
Squier:-
Affinity< $179.99
Vintage Modified< $299,99
Classic Vibe $322.99 (current sale price at GC)
Fender
Made in Mexico $599.99
Made in America $999.99 (Fender American Special) $1349.99 (Fender American Standard)
Now there are variants too that are different from the standard Jazz design - could differ because of pickup configuration or being an active bass. Too many to list, just covering some.
Model
Fender Aerodyne : $799.99 (jazz pickup and pbass .light bass/slim - Made in Japan)
Fender Blacktop : $499.99 (2 sets of P-bass pickups - Made in Mexico)
Fender Geddy Lee " $899.99 (hey, it looks like Geddy Lee's bass! - better bridge, pickups, block maple fretboard - Made in Japan)
Fender Modern Player: $499.99 (dual Modern Player humbucking Jazz Bass pickups - Made in China)
Fender Deluxe Active Jazz:$ 749.99 (active 3-band EQ combined with the standard volume and pan- made in Mexico)
There are many more but these are just to get you started. I do recommend looking at the Fender website for more detailed descriptions etc.
Used prices are much cheaper (obviously) and that's where you can get some really good deals. For example, I picked up a Made in Mexico Jazz bass used in excellent condition for $200.