14x22 is really tight quarters. With a 4 post lift you won't have enough depth for a workbench at the end. If it's only for storage, then you're fine. I'd draw the floor plan to scale and then add the lift and any benches, shelves, tool boxes, and equipment you'd likely have in there.
$14-17K sounds awfully inexpensive. For budget protection I'd add at least 10% overage, then xxxx? for unforeseen surprises.
I'd lean toward your already established space and lifting the ceiling. Potentially less disruptive to the lot size and easier to control costs.
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