O.K.
3" X 4" is quite small. So if you are going to make it much bigger you will need more detail than it actually contains. As it is a print and an old one at that, the detail will probably be a little limited to start with. Old negs were a little softer than we are used to these days. The film emulsion and the lens glass has leapt ahead since these photos were taken (I don't know about you, but even though I have no relationship to the people in the images, I could spend all day looking at old photos). and of course every time the light goes through glass it pics up the distortions from tiny imperfections in that glass. Also of course thay are prints, not the negative, So some detail will be lost in the printing ( the image has to go through another set of lenses and onto the paper which has a texture).
If you look at the "Control Panel" that your computer displays on the screen when you use your scanner. There should be an option to scan at a higher level of DPI. (I am guessing as I don't know Jasc very well , but all the other programms that I have used contain something similar). or if not, you could scan to a memory file (Maybe on the desk top or in "my photos") and then use the "Control Panel" from the Scanners software. This may offer some improvement, But in the end every time you alter something you loose a little detail, and although you can always remove detail, you can't replace it. Maybe you will just have to settle for either a reasonably sharp 3" X 4". or a softer but larger print( most images are viewed from a distance which suits the size of the print anyway. So making it larger will probably just mean that people hold it further away in order to see it).
Sorry if this has not been too helpful. Does anyone else have any ideas?
New software? Really, unless you want to be a pro photographer (When you will need Photoshop CS at about £500 a pop). there are a wealth of options. Photoshop Elements is a really good one, and a friend of mine said that for family use you can do a lot worse than Jasc ( well you should know the answer to that one...). "Nero" do photoshow express. which has a good write up. For my money ... I have always used PhotoShop since version 3. So I am a bit stuck in a rutt. But Elements is a very powerful tool and has the benifit of being very like the industry standard PhotoShop CS, so it is often easy to get answers to questions that you may have. But ultimately your buget will have to decide.
Tim.
P.S. Again, Love the photos almost a past innocence about them.
P.P.S. I know what I forgot to say...
What type of scanner do you have?.. It may shed some light on the matter ! ! (Sorry !).