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Does it still work out that if I'm not buying lenses I can get a bridge camera or aren't they a thing anymore?
If going DSLR do I just want to buy a body with decent sensor and then slap a off brand lens kit on it(what I remember doing with film back in the day)?
Clockwise-
You could get a bridge camera but it won’t be good for shooting bikes. Small sensors, slow (zoom) lenses.
You want a short tele ~ 85mm effective. And sharp results ~ f2.8. Standard on-brand f1.8 lenses will give you that and fast AF.
If you have old standard lenses that’s maybe a way to go. Pentax still use k mount. Canons can fit a range of old lenses with adapters. It can be slow getting focus and exposure sorted using old lenses as all but top end dslrs or mirrorless aren’t good for that.
miro_o
An entry level dslr. They have half frame sensors, so with a 50mm f1.8 lens you get effectively a portrait-suitable lens length. Nikon or canon.