Options:
- Traditional flat pedals - any shoe or boot; foot can occasionally slip off pedal
MTB flat pedals with pins - any shoe or boot; foot won't slip off, but the pins can make a mess of the shoe sole, or your shin, should it make contact
Toe clips & straps - shoes should not be too bulky; foot won't slip off ; need to learn to pull the foot backwards to get out, and to flip the pedal to get in. ; most pedals use the normal two bolts for the toe clips, but some pedals don't have any, and a few are non-standard
MTB clipless - special shoes must have two bolt holes, to a standard pattern; need to twist the foot to get out, and to locate the cleat to get in ; fairly normal to walk in;
Road clipless - special shoes with (usually) 3 bolt holes to a standard pattern; need to twist the foot to get out, and to locate the cleat to get in ; difficult to walk in
Hybrid flat/MTB clipless - the pedal is flat on one side for normal shoes, and MTB clips for the special shoes on the other. Usually weighted so the pedal hangs vertically, meaning that the clip side is accessed by moving the foot onto the pedal from the rear, and the flat side is accessed by drawing the foot back onto the pedal
For traditional flat pedals, there are also Power Grips, which are straps between the rear inside and front outside corners of the pedal. The foot slides in with the toe angled inwards, and the strap tightens as the foot is straightened.
Cheap shoes for MTB clipless are usually fairly flexible, which makes walking easier, but the typically small pedals can become uncomfortable on a long ride. Adequately stiff shoes are common enough, but usually aren't at the bottom of the price range
I think I'll give the Power Cords a go, as they sound exactly like what I'd like - ie a good clamp on a platform pedal, without the inconveniences of special shoes.