I claimed 9 on my W4. I just got my first check: gross was 1450 and net was 1248.66. I thought I'd get much less taken out. Does this seem correct?

If only SS and Medicare was taken out, then it would be 1450-111= 1339.

A lot depends on what your filing status is (single/married) and what your pay cycle is.  And even then, it may tak a couple pay cycles for Paroll to enact a change to a W-4.
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Check the tables starting on page 46 here to see what to expect for the income tax withholding portion

<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p15.pdf">https://www.irs.gov/pub/irs-pdf/p15.pdf</a>

Yes, as you must still have Social Security abnd Medicare payroll taxes withheld, as well as any applicable state taxes, employee benefits, etc.  Check with your payroll dept for details.

Some states also have mandatory state disability insurance, unemployment comp, and similar employee withholding.

Thanks so much. I'm married and live in NY. The breakdown on my check is: federal income tax: 62.70, ss tax: 89.90, Medicare tax: 21.03, and NY State Worked In: 27.62.

Is the 1450 your weekly gross pay?  Semimonthly?

Those figures appear to be correct for a weekly gross pay of $1450. See page 49 here:
<a rel="nofollow" target="_blank" href="https://www.irs.gov/pub/irs-pdf/p15.pdf">https://www.irs.gov/pub/irs-pdf/p15.pdf</a>