Belly,
You chose a good press and system within your monetary criteria. For the money, there isn't anything better. That being said, there are better presses, but the cost would be much, much more. Good choice!
Unique will be a good choice for the calibers you have mentioned. It will give you mid-range loads that will not be hard on your 70 year old body.
One question, how are you going to do your priming? The kit that is on the Lee webpage doesn't have a priming tool with it. Did the kit you bought come with one? If not may I suggest the "Lee Safety Prime for Classic Cast & Turret Press ". It will make loading that much faster. If you don't use that you will have to place a single primer in the holder each time you need to set one. Very time consuming and could be a problem if you have oily hands, not to mention the mess if you spill them on the floor! The hand tool is useful as well but sidesteps one of the benefits of having the turret press.
Also, using Unique with the powder measure and disks that come with the kit may cause a problem. You will not be able to "fine tune" a load with the fixed disks. It will work, as long as you use a large enough load, 7 or 8gr of Unique, and go slow. The flakes are so big with Unique that it can "bridge" gaps. Another suggestion for the future is the "Adjustable Charge Bar". That way you can "tweak" a load if necessary.
There is another benefit to using Lee equipment. They have videos on their website for setting up and running their equipment! Here:http://www.leeprecision.com/cgi/catalog/browse.cgi?1228399009.3178=/html/HelpVideos/video.html
At any rate, have fun and be safe. You have the tools to make some good handloads.