What plastics are safe/useful to melt?

Many plastics can be used for melting, but not all. Basically there are 2 types to distinguish here; thermoplastics and thermosetting plastics.

Thermoplastics can be heated and shaped. Examples are HDPE, LDPE, PLA, and PP (see the Wikipedia link for a longer list of types)

Thermosetting plastics harden or burn when heated. Examples are Phenolic (PF) resins, most polyurethanes (PUR) and some types of polyester.

Note that melting plastic can release toxic fumes. How toxic the fumes are depends on the type of plastic. I would not recommend melting PVC, ABS or PS. I heard mixed stories about PET, I guess it depends on the used additives. In any case make sure you have good ventilation when you melt.

Food grade plastics are plastics that contain very little contaminants like dyes or other additives. To guarantee a plastic is food safe, it's usually made from virgin (non-recycled) plastic. The exception is PET bottles. When collected separately they can be reused or recycled into new PET bottles. Whether your molded plates are food grade depends on how well you can control the temperature while melting (keep it as low as possible) and if you introduce contaminants or not. The safest to use is probably HDPE. In any case I would not put your plates in a dish washer or microwave, or use them with acidic foods like tomato sauce.

There is more information also here:

• Other Sustainability SE question: Can I recycle plastics at home by melting and molding?
• Chemistry SE question: Does melting HDPE plastic produce toxic fumes? (melting, not burning)