We will be having kids soon and I wanted to start poking around and finding out a few things from more experienced parents in this area. My questions:

How old should a child be before they can come with me on a bike ride (on my bike, not there's)?

What set up is the best for a kid on my bike? Pulled in a trailer? Back seat attached to my bike? Front loaded seat on the bike?

Do we need a different bike to haul a child around in?

What other issues should we know beforehand?

Thank you.

I think the official (or at least common) recommendation is no younger than 1 year. But really it is all about the ability of their neck to support their head and helmet, combined with the force of a fall. So, that could be younger or older. I felt comfortable enough taking my daughter out when she was 9mo, but a friend waited until their kid was closer to 14mo. Also consider the weight of helmet they wear, as some are noticeably heavier than others. Those super cute Nutcase helmets are HEAVY.

For carrying, there is no best solution, as each has pros and cons. For just one kid, my favorite is front mounted (legs go around the stem/steer). You always can see them, they can see the world coming at them, and you're able to talk with (to) them easier. Cons are that depending on your bike, it can be a little awkward to pedal, particularly if you're trying to tackle some hills. Also the center of gravity of your bike is quite high and even with a nice double leg kickstand, you'll be in constant danger of a tip over. Just requires diligence.

Rear mount gives up the easy interaction and forward views, but keeps the tipping issue. It does allow more natural pedaling and for a heavier kid. Trailers were never a consideration for me. Some people love them, but I consider them a bike path and cul-de-sac biking solution. I feel comfortable biking on nearly any normal street with a bike lane with my kid on my bike, but would be really anxious about towing them around behind me with any sort of traffic around. But, it does allow you to have a very stable configuration, and to either carry two kids or a kid with some groceries.

By far, the best kid carrying solution to me is a dedicated cargo bike, particularly the front loading style. But, that is a huge upfront cost, and could be total overkill for your needs. I have another kid on the way and plan to bike with them immediately, plopping their car seat right into the cargo box. Still leaves room for my other kid, diaper bag, etc.

I used a chariot trailer for our first kid, I used it with the infant sling from the time he was about 3 months old. Our second kid was in a bakfiets from birth and then the Cetma when we got it. Your biggest obstacle is going to be busybodies telling you how you are endangering your child from exhaust, car crashes, cold, abduction and a myriad of other threats.
Front loading cargo bikes are great for hauling kids around. I would buy one even if I didn't have kids to haul in it. My kids very seldom ride in it anymore, but I still keep it and use it almost daily for hauling things around.
Much as I use my Cetma, I could not call it necessary. It does pay for itself in deferred car expenses so it is worthwhile.

Unless the baby is in a carseat, the earliest they should ride is probably 9 months or so. I agree with Nightdiver that helmet weight is an important consideration for biking with babies. Using a carseat is possible with a trailer or a front-loading cargo bike or a Madsen "bucket" bike. There's also the Steco Baby Mee that mounts to a standard rear rack, but I think that solution is more likely to get you noticed by police (assuming you're in a jurisdiction that requires helmets for kids): Steco Baby-Mee child seat support

Once they can sit up, I highly recommend front seats, even if you have to get a new bike with a longer effective top tube to give you more space--they're just so much fun. Rear seat would be my second choice, followed by trailers. Cargo bikes aren't really a "need" until you have two kids.

Do you have a pic of your set up?

do you happen to have a picture of your setup?

Here is a picture of my setup from 32 years ago. Twins are about nine months old. Worked just fine.
I've been informed that my grandson, sleepy boy's son, will wear a helmet when riding until he is 18 years old.

I don't have many pictures of the baby in the bike, they were usually under the cover of the chariot or I was concentrating on riding. I used to use a carseat or a bugaboo stroller strapped into the bucket of the bike when she was a little baby.
here is one from her toddler years.
https://flic.kr/p/7tN3mc