Hi - what a sad time for you,
We've just introduced a second dog into our family last week and that was because we could be faceing the fact of losing our border collie within the next few years or so. We ended up having a rescue cocker from Many Tears.
The best thing i can say is make sure you are 110% ready to add a new dog into your life. Then when introducing a new dog for the first time - take your dog for a walk first before the introduction to drain some energy, then take them both for a good walk together, and i mean just walk - at quite a quick pace. And then they will hopefully they will accept each other a lot better and quicker.
A word of caution though if you are seriously thinging of taking on a rescue dog, they are not a quick fix to replacing the dog that was lost (but hopefully you are alredy aware of that). We've just taken on a ex-breeding bitch who was never been housetrained, never walked on a lead, never been in a house and heard a hoover etc, never known how to play - they are a lot of work, and a lot of time and commitment is needed.
best of luck finding your new friend