I want to upgrade from bit Mojave 10.14.6 to Montery but have the following questions and concerns:

[Craig29183371jg5a]

I want to upgrade from bit Mojave 10.14.6 to Montery but have the following questions and concerns:

1. I don’t want to loose my photo files saved in jpg, psd, tiff and quickdraw / pict file formats. 

2. CS3 is currently installed and working in 10.14.6.

3. What is the best approach to keep the photos? Can I install  Lightroom +/or PS Elements on 10.14.6 and then upgrade to Monterey. 

4. I really don’t want to subscribe to latest full Adobe CS due to cost. 

5. Ideally just looking for a photo management app that will catalog and keep my preexisting photos as well as new

[Nancy OShea]

Get a new computer. If you're still using CS3, your computer hardware probably isn't sufficient to run Monterey or Ventura.

OPTION 1: Backup your work files to an external drive or USB stick. 

OPTION 2: Use a dedicated backup & recovery service like Blackblaze that automatically copies files to the cloud each night.  When you migrate to a new computer, you can easily recover your old work files to the new computer.

NOTE:  CS3 is dead.  It cannot be installed or activated on a new computer.

MODERN OPTIONS:
Photoshop Elements (no subscription needed).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:

• Photoshop CC and Photoshop on iPad
• Camera Raw
• Lightroom on desktop, mobile and the web
• Lightroom Classic
• Portfolio website + hosting
• Adobe Express (free starter plan)
• Bridge
• 20 GB cloud storage (upgradable to 1 TB).
• Free upgrades for paid subscribers

https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (51 + pro apps & services) and Single App Plans
https://www.adobe.com/creativecloud/plans.html

[kglad]

you won't be able to use ca3 on any other computer. ie, you can't reinstall and use it beyond the 30 day trial period.

your data (eg, photos can be transferred without problem).

[John Waller]

I would personally not worry about upgrading that old Mac to Monterey. You won't gain much but you could encounter a host of incompatibility problems due to the aging hardware.

As @Nancy OShea says, get a new Mac when you really need the latest macOS (currently Ventura) or your current Mac eventually stops working.