Change the email address associated with an APPLE ID

You have an Apple ID which is a Gmail address and I gather you have also created an iCloud address as part of it.

In this instance, you can change the ID login address to the iCloud address. However I would recommend you consider not doint this because if you are using the iCloud as a working email address you would also be announcing what your login is to the world which reduces your security. It's better to have as the login a separate address which you don't use for anything else.

If you do change to the iCloud address you must use a different address as the 'rescue address' or if the account goes wrong in some way Apple won't be able to contact you - for example to send a reset email.

This is the process for changing the ID address:

1. Firstly, sign out of iCloud on all your devices: go to each of your devices and sign out in System Preferences (or Settings)>iCloud - 'Sign out' on a Mac, 'Delete this account' on an iOS device (this will not delete the account from the server). If you have 'Find My iPhone' etc enabled you will need to disable it first. Your synced data will disappear from your devices but will reappear when you sign back in.
2. Create a new email address, for example at Yahoo or Gmail, or anywhere convenient (or you can use an existing address as long as it is not associated with an Apple ID). Or you can change it to another Apple address but only if it's listed when you click the link to change (in practice this means your main @icloud.com address, and the equivalent @me.com and @mac.com versions if you have them: it does not include email aliases).
3. Go to http://appleid.apple.com and click 'Manage your Apple ID'. Sign in with the current ID.
4. Where it says 'Apple ID' and gives your current ID email address, click 'Change your Apple ID'.
5. Enter your new address and click 'Save changes'
6. Sign back into iCloud on all your devices with the new ID and password. Your synced data will reappear (give it time).

I reiterate - before you start, sign out of iCloud on all your devices. Failure to do this will lead you into difficulties.

This process will not affect your purchases since you are not changing the ID itself but only the name of the ID (think Umberto Eco - the name of a thing is not the thing itself) - with which piece of existentialism I will wish you good luck in your process.

Reference the 30 days.

Under your Apple ID, click Change Apple ID. If you try to change your Apple ID to an @icloud.com email address created within the last 30 days, you might be asked to try again later.

Apple ID Name Change

I don't know about the 30 days, I suppose it's possible. My account page is probably different from what you have as my ID is already an Apple address (dating from the pre-iCloud days) - so I can only change it to the ones shown here:

You should see something similar. If none of this works for you, I would suggest that for the time being you create a free email address - Yahoo perhaps - and change to that, since your ID should really be a working email. Then perhaps wait the 30 days from the creation of your iCloud account on the off-chance and try again. If you can't get it to work you should contact Support: https://getsupport.apple.com

If Apple delete an account you will lose all your purchases made with that ID. 'Recreating it' won't work: you won't be able to reuse the existing addrtess or the same iCloud address and you will be creating a new Apple ID which won't allow access to your purchases and updates.

Regarding the account we have been talking about, I don't know why you aren't seeing the same options (without the @mac.com and @me.com variants since you won't have those). It might be the 30 days thing, though I emphasize I don't knokw anything about that or whether it even exists.