My current database stores these two fields as integers, but might be better if they are store as Strings so no conversion would be needed.

Would that be the correct path?

yes
not all phone numbers are (999) 999 9999
similarly not all postal codes are numeric

UNLESS you see you application as specific to one geographic location and you never see a requirement to store inforamtion form outside that geographic location

IF you know that all your rows containing addresses are US based then a integer may be reasonable

If you know that all your rows containing phone numbers are North American then you can use the (999) 999 9999 format

On phone numbers irrespective of where you are are I think you need to separate any exchange / area codes.

Arguably you could consider pre-pending the international number prefix (eg +1 or +44.. although that can be derived assuming that you store the country separately. In my books it used to be a cunning trick to equate the country name with its international country code.. that was until so many counties started using the 001 prefix.

unless you plan to retrieve the average phone number or average zip code for some group, there is no point in using a numeric datatype

If you don't add it, subtract it, multiply it, or divide it, then it is a string even if it looks like a number.

Ditto. Maybe throw in some sort of check constraint if you want to ensure people do not enter things like "see x person's phone number". They will if you let 'em

pootle flump ur codings are working excelent.

oh! oh! a CHECK constraint!

this puts you in the "database mensa" category -- the top 2% of database practitioners, who not only know what a CHECK constaint is, but when to use one

full marks, pootle

Pfff - that's nothing. Normally I create a table of all the possible phone numbers and create a foreign key

Awwww

pootle flump ur codings are working excelent.

hold on a sec -- do you foreign key all your phone number digits to a digits table?

(if i may be permitted to use "foreign key" as a verb)

if not, you have not fully normalized your phone numbers

some purists, blindman among them, if i recall, then further foreign key their digits to a bit table