In addition to my collection of skulls, I've collected several rats over the years - some of them expensive, but some of them just the typical Dollar Store variety. Here are a few basic enhancements that can be made easily to bring them up to a more realistic level.
Step 1: Supplies and Tools
Dollar Store (or the equivalent cheap-goods store in your country) plastic rat
Whisk broom - black bristles, again from the dollar store.
Craft needles - regular needles may be too thin, so get some heavier duty ones. My dollar store had these too!
Wooden dowel - size that fits comfortably in your hand. You may also use the handle of a wooden spoon, I think the dollar store sells those too.
Small side cutting pliers. Guess where you can get them if you don't have some already? :-)
Small bottle/tube of liquid latex - places that sell Halloween makeup usually have this, so try your pharmacy, department store, or your favourite Halloween store, or possibly even the dollar store - you don't need much.
Gloss Mod Podge or other GLOSS sealant - your craft store should have this, though check at your dollar store in the craft aisle.