[EDIT]: I may have overthought things. Try what usasma said first and if that fails then consider the thoughts below.
1) Once I install the new hard drive, I want to do a fresh install of Windows 7 x64. Will I have to start with their original OS, Windows Vista? (Note: I do not have a recovery disk, so it will be a fresh install). Will I also need to update the BIOS, and/or make some other software/firmware change?
Pavillion dv6700t: There are reports that you cannot do a fresh install to Windows 7 (schang105, 2012) as people will get an error code 0x80300001. Problem lies in a stripped down Phoenix BIOS that only supports AHCI and not IDE natively. HP confirms that models that ship with Vista do not have the ability to use IDE (HP Notebook PCs - How to Add Serial ATA (SATA) Drives to a Windows Installation, n.d.). schang105 (2012) provides the solution of cloning the drive in order to move things over. This this put things in a much harder scenario even if you are to try to install Vista as a fresh install, you will still need the storage drivers that are "textmode". HP provides the following guide for installing native Serial ATA by extracting drivers or downloading them from HP or the chipset manufacturer (HP Notebook PCs - How to Add Serial ATA (SATA) Drives to a Windows Installation, n.d.). This probably is your best bet. As soon as you can get Windows 7 on and activated with a valid key, the jump to Windows 10 should work fine.
HP/Compaq 6730b: HP has officially stated that no Windows 7 drivers will be released (HP Notebook PCs - Windows 7 Upgrade Options for Notebook PCs, (n.d.). You may be able to find and coax on Vista x64 or Windows 7 x64 drivers. One place to look would be driverpacks.net. These drivers are to the best of my knowledge used after Windows is installed. I used these a lot back during the Windows XP days downgrading Vista machines.
2) Once I have Windows 7 x64 installed on the new drive without issue(s), could/should I attempt to upgrade to Windows 10?
Once you have Windows 7 x64 installed fined, I would recommend taking an image backup. You can use Windows Image backup, Acronis, Ghost, Macrium Reflect, or some other imaging software. After that, try to goto Windows 10. If things fail horribly, at least you can roll back using your image backup.
I hope this helps!
schang105. (2012). How to enable AHCI in HP pavillion dv6700t [Msg 5]. Message posted to http://h30434.www3.hp.com/t5/Notebook-Operating-System-and-Recovery/How-to-enable-AHCI-in-HP-pavilion-dv6700t/td-p/1401997
HP Notebook PCs - How to Add Serial ATA (SATA) Drives to a Windows Installation. (n.d.). Retrieved from http://support.hp.com/us-en/document/c00758841#standalone
HP Notebook PCs - Windows 7 Upgrade Options for Notebook PCs. (n.d.). Retrieved from http://support.hp.com/us-en/document/c01859348
Edited by ZeroForge, 15 July 2016 - 09:31 PM.