What type of printer should I use for cardstock?
Your question is somewhat broad-ranging and is usually discouraged on Stack Exchange forums. Your last question certainly fits that bill. Those answers can be found by searching for reviews of possible candidate printers within your budget.

More specifically, you would be seeking a printer with a relatively flat paper path, to prevent jams caused by thicker paper as is typical of greeting card stock. Both ink-jet and laser printers will be found in this form.

Ink-jet printers will be more expensive for ink (consumables) and have lower throughput ratings than a laser printer. Look for duty cycle information and compare across your budget selection.

Ink-jet printers are usually recognized as having cost-per-page in the range of $0.05 to $0.15 while laser printers can run below $0.05 per page. I would add a reference to this, but the search for that reference generated thousands of links, all of them rather voluminous.

If you do not need photograph reproduction of images, a color laser will give you higher production rates due to the page per minute rating of this type o printer. A toner cartridge (four in a color laser) will last much longer than an ink cartridge.

On the other hand, there are bottle-fed inkjet printers that have a flat paper path and low consumable costs. This is accomplished by designing the printer to use stationary high-capacity ink bottles mounted on the housing, feeding the print head with hoses/tubing.

There is no easy answer to your question.