Hi 
Practically you need -
An age gap of at least 2 years but preferably a bit more between your youngest birth child and the new adoptive child. This means your BC realistically needs to be at least 3 before you begin the process, but many agencies may say 4/5 years old (so you can be approved for a child aged 0-2)
A spare bedroom for the new child
The ability to take time off work - 6-12 months, agencies prefer 12 but can be flexible, but aim for 6 months minimum (it's possible to return to work earlier but it's not considered ideal)
In terms of your age, as long as you are both under about 48-50 there shouldn't be an issue with most agencies, some will let even older people adopt (for instance in my LA a 55 year old could adopt a school aged child)
Most past convictions are not barriers and are looked at as part of the assessment
Many adoptive parents have health issues, past histories of depression etc. Having health issues is not a barrier, but again on a case by case basis unless it's a very serious issue
A support network around you