Choosing a camera comes down to two decisions: body type and sensor size — and neither needs to be complicated.
Body type: Mirrorless is where things stand today — every major manufacturer builds their newest lenses for mirrorless mounts first, autofocus is faster, and what you see in the viewfinder closely matches your actual exposure. DSLRs still work fine if you already own one, but the major brands have largely stopped developing new lenses for them. Compact cameras trade creative control for pocketability — fine if that's genuinely your priority, limiting if you want control over background blur or low light.
Sensor size: Full-frame gives the best low-light performance and shallowest background blur, but costs accordingly. APS-C — smaller, cheaper, found in most beginner cameras — teaches you everything about exposure and composition a full-frame body would. Micro Four Thirds goes smaller still, trading some low-light capability for a lighter kit.
Full-frame means a sensor the size of a 35mm film frame, 36 × 24mm. A smaller sensor's crop factor says how much smaller its diagonal is: about 1.5× for APS-C (1.6× on Canon), and 2× for Micro Four Thirds. Multiply a lens's focal length by the crop factor to get its full-frame equivalent — a 35mm lens on a 1.5× APS-C body frames roughly like a 52mm lens on full-frame. The lens itself hasn't changed; the smaller sensor simply records a smaller part of the image the lens projects. The Crop Factor Calculator converts in either direction for any format.
Background blur and low-light performance follow from the same geometry. To get the same framing on a smaller sensor you use a shorter focal length or stand further back, and both give more depth of field at the same f-number. That's why a full-frame camera at f/2.8 blurs a background more than an APS-C camera at f/2.8 framing the same shot. In low light, a larger sensor collects more total light at the same settings, so at the same ISO its images generally show less visible noise. In good light, neither difference matters much, and a lens with a wider maximum aperture can make up for a lot of both.
One more thing worth knowing: megapixel count matters far less than marketing suggests. Modern budget cameras sit around 20-26MP — more than enough for large prints and cropping. Chasing higher numbers isn't where your photos will actually improve.
Someone who mainly photographs their children indoors and on weekend trips compares two options at a similar total cost: a full-frame body with a basic kit zoom, or an APS-C body with a kit zoom plus a 35mm f/1.8 prime. On paper the full-frame camera is better in low light. In practice the APS-C kit suits this person better. Against a kit zoom at around f/4.5, the f/1.8 prime lets in about two and a half stops more light, which more than makes up for the roughly one-stop sensor-size difference indoors, and it gives the softer backgrounds they wanted. The full-frame body with only the slower zoom would leave them shooting at higher ISO, with busier backgrounds.
The takeaway: unless you already own a DSLR, start mirrorless, and don't feel pressure toward full-frame as a beginner — APS-C is genuinely enough to learn on, and you can always move up later once you know what you actually shoot.