For home defense you really want long guns if possible.

If the up-front cost is a big issue then shotguns are likely to be more attractive than rifles (or even pistols for that matter).

Shotguns are also fun for clay shooting and extremely versatile for hunting.

An AR15-style rifle would also be quite effective but I am imagining you're looking at $1,000 or more to get into an AR.

There are two things I'd encourage a beginner to consider for handguns:

1) If you get a centerfire handgun with a "double action" (where the trigger both cocks the hammer and then releases it) that will be very good for dry fire (training by pulling the trigger without ammo in the gun)

2) If you get a rimfire handgun (like a revolver in .22 LR) that will be very good for live fire because the ammo is very cheap (at least here) and you can train a lot

You can also do dry fire training with .22LR but it needs to be a gun designed for it and/or you need something in the chamber that's softer than steel that the hammer can hit (a specially-made product or just drywall anchors)