I was in a similar situation a few months ago. My wife got me a PSPgo for Christmas, and I was trying to look through PSN to find things worth getting.
At first I was discouraged because several games I had been interested in weren't available, but I looked around and found more than enough things to keep me busy. I also have a soft spot for digital distribution, as I hate having to pop in or carry around discs (I get almost everything on my PC via steam/impulse now).
As you like strategy games you may want to look at:
Disgaea (1 or 2)
Wild Arms XF (though people seem very polarized on this one)
ZHP (Zettai Hero Project)
You could also pick up ps1 classics, like FFT
The PSN store updates every tuesday, so you can check their blog for new sales/price drops then. Generally the best deals I have seen are around holidays, or when a specific publisher has a sale week (got the Sega deals, Phantasy Star Portable 2 and Valkyria Chronicles 2 for $16 each around Christmas; and picked up more Atlus games than I probably should have during their last sale).
As for specific games, I recently finished Jeanne d'arc and really enjoyed it, though I didn't think I would when first starting out.
Just last week I started playing FF7 again in an effort to revisit some old ps1 classics. I remember many of them as good, but was curious to see if that was just my fond memories and rose-colored glasses, and how well they stood the test of time. So far I find these 'epic' big name ps1 games go well interspersed with other psp games, as they have a weightier feel that you don't often get from portable rpgs which tend not to take themselves as seriously (though that of course depends on the game) and I like the variety.