Here are my suggestions for the starting frigates.
Every frigate : Fit the Augmented Engines hull mod, it will allow you to control most fights since you can break off and vent your flux safely when you need to. It also makes you faster when travelling on the campaign map. Remove your missiles if you plan on having any prolonged fights because all small missile racks have only 3 missiles maximum, except the Swarmers (anti-fighter). If you have any spare ordinance points, put them in flux vents.
Hound : no suggestion, I never started with it and it has no shield, making it very weak. While it could be a fun challenge for an experienced player to start with this, as a newbie you should probably recreate your captain until you get something better.
Vigilance : A fine starting frigate. The stock Pulse laser is very good. Unlimited ammo and good range. You want a good number of flux vents so you can fire it for longer. Ditch the missiles. Kill enemy frigates from outside their weapon range.
Lasher : Also fine starting frigate. If you have Vulcan autocannons then you may want to replace them with light machineguns. Vulcans are rather short on ammo. Ditch the missiles and the expanded missile rack hull mod. Get the Expanded Magazines mod (and Augmented Engines as always). If you can, buy 2 Railguns and fit them in your hardpoint mounts (the ones that can only point forward). Set your light machineguns to autofire and use the railguns to easily overload most shields aswell as to safely snipe people. Railguns and light machineguns both have a very good ammo quantity if you use Expanded Magazines.
Wolf : I never started with the Wolf but I can already tell you it's probably the most powerful frigate to start with. Since I never played it I guess I'll let other people teach you how to do so, or perhaps you can come up with something based on my suggestions for the Vigilance and Lasher.
