Reliable car under $3,000?

Under $3,000, your realistic option from the data is the Honda Civic, but only if you target the right model years and accept known risks. The Toyota Corolla and Mazda 3 have no owner data for vehicles in your price range, so there is nothing concrete to recommend them on. The Civic has documented problems that cluster in specific generations, so your choice comes down to avoiding those.

For the Civic, the data flags two major trouble spots. The 7th generation (2001-2005) has recurrent head gasket failures on the 1.8L D17 engine, which can kill the car quickly. The 8th generation (2006-2009) has isolated but severe cracked engine blocks on the 1.8L R18, plus poor paint and significant blind spots. Rust is a recurrent issue across older generations, so check the undercarriage and wheel wells before buying. If you find a 2006-2009 Civic, the engine block risk is isolated, not universal, but you need a mechanic to inspect for cracks and rust. The 1.5L turbo engine concerns and CVT issues apply to newer models, which are far outside your budget.

Price reality: the Civic data covers 2014-2026 models, with a median around $21,796. That means the data does not include prices for the older generations you can afford. So you are relying on the owner-reported issues, not price guidance. For a student needing a few years of service, a well-maintained 2006-2009 Civic with a manual transmission and no rust could work, but you must budget for potential engine repairs. The head gasket issue on 2001-2005 models is too frequent to recommend.

Given your situation, the safest path is a 2006-2009 Civic with a manual gearbox, a clean rust inspection, and a documented service history. Avoid the 7th generation entirely. If you cannot find one that passes a mechanic's check, the data does not support any other vehicle in your budget, so you would need to stretch your budget or wait for a better example.