Most hand made pens will use one of four basic types of refills. There are pros and cons for each, and what people like best varies widely.
Cross Style Pens
The Cross company has been around for 170 years, and have been making ballpoint pens since ballpoints have been made. Many people like Cross-style pens because it is the thinnest of the common refills, allowing for a slender pen look and feel. Cross brand refills are found at most office supply stores, but tend to be a bit pricey.
Parker Style Pens
Parker refills are thicker than Cross, generally resulting in a somewhat fatter pen. You will get a lot more mileage ink-wise out of a Parker style refill than a Cross. In addition, there are many more options in terms of compatible brands and types of inks than for a Cross. If you're a gel pen fan, they are readily available in Parker style refills. One other selling point is that most of the Parker compatible refills are less expensive than Cross refills.
Rollerballs use a liquid based ink. Much thinner than a ballpoint ink, they require less pressure than even a gel ink. Rollerball ink takes longer to dry and is pickier about paper (they can bleed through some very thin papers.) If you like the look and feel of writing with a fountain pen but don't want the hassle, the rollerball pen is a nice compromise.
Fountain pens are a category in and of themselves. A fountain pen uses a split nib to apply a water-based ink to the paper. Unlike older traditional fountain pens where the nib was dipped into the ink, modern fountain pens use a cartridge. Cartridges can be either replaceable or refillable. Learning to use fountain pens is an art in and of itself, and will be covered in a separate entry.