Bellavinci I also think you need to think why it is so important to you now to have the family within the next few years having been in a relationship for quite a long time. I am not asking to be nosy, and you do not need to say here, I just think you need to understand your own motivation because your social worker will want to understand what makes you tick.
In terms of time frame you will need to factor in 6 months of non-fertility treatment before you start the process for adoption (check with your local authority how long it needs to be, six months seems to be pretty standard, IMHO). Then you will need to be assessed which could take 6 months (or 6-12 months) and then matching which could take a day or a year, but to be honest if you are willing to consider a sibling group aged 3-10 I expect you would not wait long.
I think you also need to consider having experience of looking after children, outside the family (not nieces and nephews) and your DH will need that too, I am not sure but IMHO most likely you will both need to show experience of working with kids in some capacity,voluntary - toddler group, school group, Cubs or Brownies etc).
I do recommend counselling, for both of you. To come to terms with not having a biological child. Your fertility clinic should offer it and it may be free. We had three free sessions and I also got some free from my GP surgery too!
The reason it is important to be sure you are comfortable with your decision not to pursue a biological child is not just for you or your DH or you as a couple but to ensure when you open your heart and home to your 3 and 10 year old, or 4 and 7 year old, or baby or whoever you adopt, that you will be able to be fully embrace your new parenthood and not have regrets about not having more treatment (IMHO)!
It it is possible that the counselling and the experience with kids can happen while you are still having fertility treatment or in your 6 months gap after treatment. Then within a year of the start of the process you may well have a family! I know people who it happened very quickly for. For us it took a bit longer, 20 months plus the 6 months wait at the beginning but I think that was because we have a birth child and we started before the time frame moved from 12 months to 6 months for approval. So I am not sure that counts as a 'few years'.
Good luck.