I'm looking at motorcycle padding/football equipment/plastic faceguards because I'm on a budget. Are they safe?

Short answer: no.

Motorcycle pads are designed to protect you against abrasion and falls on large surface areas. They're not intended for thin edged steel. There are too many gaps, and in those gaps, there is *no* protection.

Some people start to think they can augment these pads into making them safer, but given the effort and money you'd put into it,  you're coming very close to buying a HEMA jacket in cost.

There are a number of jackets that can be had for at or under $200 USD, and they'll keep you safe.

Especially when you're new, you don't have the control or ability to keep you or your sparring partner safe. If you're starting up a study group in a park, you're better off at slow play with basic fencing masks (which can be had for around $60), and slowly building up gear. 

You have to remember that  you are practicing martial arts, and it's very easy for adrenaline to take over and cause yourself real harm.  And most HEMA insurance won't cover you if you're using inadequate gear.