You can't go wrong if you stay with the LBVs; those designated Late Bottled Vintage. Try Taylor-Fladgate, Dow, Cockburn, Fonseca, Warre or Graham.
In a nutshell LBV is port from a single harvest in a year designated as vintage by the Port Wine Institute. Instead of maturing in barrels for two years like Vintage Port, LBV is aged from four to six years and then is bottled and ready for drinking. With Vintage Port, not LBV, you'll generally want to wait ten to twenty years before decanting and drinking.
Truthfully, I've always preferred LBV to all ports.
But, here's the rub. Since 1991, the Port Wine Institute has called damn near every year a vintage year. 1994 was considered by all to be the vintage of the century and even the LBV is trading at $55+ when you can find a bottle. You should be able to find '96s and 99s at reasonable prices.
I just checked a site I often use and they have WARRE 95 LBV PORT 750, WARRES 92 CROP LATE BOTTLED VINTAGE PORTO (bottled '95) for $21.97.
I've tried the Aussie ports, like the highly acclaimed Whisker's Blake, but I don't care for the lack of body.
What ever you do, stay away from the cheap wino ports. There are currently some new CA ports that are getting some notice, but I have not tried them.