integrated amp question

As long as your integrated has a direct input to the power amp section, you
can take your time hunting down your new gear, and add what you like
whenever you find it. The advantage being, of course, that you can spread out
the purchases: phono stage, line preamp, cables. The last buy would be the
power amp, and you would sell the integrated to help pay for that.

There's no particular reason to sell the integrated now, unless you happen
just to have found a crazy-good deal on everything you want.

If the integrated does not have that input to the power amp, then you will
have to consider starting your upgrades with a new phono stage and cable.
(You will be able to plug the phono stage output into an input on the
integrated.) Later, you would get both your separates--amp, preamp and
interconnect cable--at the same time, and sell your integrated amp.

depends on your integrated. many built in phono stages are quite good.

I took almost the same path as you when I upgraded. I was using an NAD receiver with preout/powerin jacks and a phono stage. First came a new power amp, using the NAD as the preamp and phono. Then a tube preamp, using the NAD only for the phono through the tape outputs. Then finally an outboard phono stage. Only then did I clean up the NAD and sell it. It performed for 20 years, and admirably right up to the end.

You'll probably end up with all separates just as I did, but there's no reason you have to do it all at once.