I have attached many things to my bike. Alas I only have a few sample pictures, to help illustrate everything I have learned so far:
fig1. This is a trailer I made:
fig2. These are some alternate Tesco boxes:
fig3. This is how I improvised with tape to attach wood and metal onto the rack:
fig4. This is an improvised basket after the standard "Decathlon Modular System" basket broke:
The first thing I used was the panniers as seen in fig1, for a DOE (Duke of Edinburgh Award) cycling expedition; they were insufficient, so a tent, a carrimat (rolled up foam for under a sleeping bag) and a backpack was place on top of the bulging panniers and held down with bungees. As the panniers were equally bulging, almost anything could be securely held on with bungees.
When I started doing Tesco (a supermarket) shopping on the back, I put all heavy items into the panniers, and bulky lighter items such as bread, vegetables, tissues etc, I would stack into cardboard boxes as seen in fig2 - as I went round shopping. These boxes can sometimes be procured if you go to Tesco at 2am to shop; they throw them away otherwise (found in vegetables isles), and they are very good for stacking, sturdy, very light and FREE. When these are stacked, they can be balances across two bulging panniers, and provided you use enough bungee cords (i recommend the carabiner ended ones rather than hook-ended ones, you can get the carabiner ended ones from Poundland (a discount-store) sometimes, they vary in length and size and quality) you can securely attach your shopping, but don't go over bumps too fast, and don't tilt too much as your centre of gravity is somewhat raised despite keeping heavy things in the panniers.
Prior to using those boxes, I must admit I used a lot of plastic electrical insulation tape, which is cheap - provided you multi-layer it, it is very strong and good for short journeys. It can be used to improvise almost anything onto a bike, though it is time consuming - fig3. (Those are rolled hollow section metal bars, and some boards of wood). I had some bad experiences with tape before discovering the cardboard boxes, mostly I ran out when trying to secure two discounted boxes of 36 packs of hobnobs (biscuits/cookies) onto the top of an already sizeable shop. They kept falling as I had not enough tape; ultimately I put my coat around them and tied the arms around the seat to hold them on. The shops I did were for 4 students, once a week - a lot of food.
Entering the world of work, I figured I needed something more professional. Naturally I reminisced back to my previous experiences, and decided I would bungee tie my laptop bag onto the top of a rear basket, a basket which contained tools. I figured the sides of the basket would have sufficient 'bite' to grip my padded bag with the bungees. They did, but Decathlon's modular system basket was crushed over time; so I had to improvise a new basket on. A shopping basket seemed ideal, but they are expensive; so i used a dish-drying rack. That broke, so I got a chunkier one. Broke. Got an aluminium one, tried to solder the joints with electrical solder and it just ran off; progressed to glue gun which worked until the shaking caused the glue to fall off and the welds popped.
Once the recycling men did not come, so I used straps to attach the wheelie bin by the handles to the back of my bike, and thus towed it like a very noisy trailer and got some funny looks.
My most ambitious project was making the trailer seen in fig1, the metal I used was too thick so it was very heavy, and although the articulated joint I devised worked very well - the way it attached to the bike was a bit fiddly. You need to be very mindful of your increased width and lessened reversing ability! Snaking can occur when going downhill. The actual construction was quite a lot of work, I would advise against it unless you enjoy making things; as you might be left with only those memories and a not very useful trailer.
Currently I attached the top part of a rack to another rack to allow me to put XL double panniers far back from where my feet can hit them. If I were to shop with those, I would acquire some of those cardboard boxes and carefully strap 3-4 to the top.
I regret, very much, that I did not take more pictures. But I really doing it!
In summary, if you want to move a lot of shopping, and don't want a trailer, I would recommend large panniers with a couple of those stackable cardboard boxes on top, and a roll of tape in case you need to improvise attaching a bargain.