This is just my opinion based on my personal experience...
It's best to do it all at once if you can. This not only maximizes the benefits but also makes it obvious that paleo is making a real difference in your life. The motivational aspect of doing it this way is phenomenal.
If you wish, set a time limit. Say that you're going to do all out paleo for 4 weeks. This makes it easier to adapt psychologically because you know there's an end date. Once you get to that end date, the benefits will likely be so clear that there will be no going back to your pre-paleo habits.
If you wish to do a phase-in, start with diet. This has the biggest impact by far. You can get started just by avoiding grains and not fearing fat. Once you see the benefits of those changes, you'll start integrating the other aspects.
I think it is OK to phase in the changes to a Paleo style diet. You can gain about half of the benefits by just cutting our refined sugars, sugary drinks, fruit juices, candy etc. from your diet. For some people the initial cravings may be overwhelming, so taking a few types of food out of your diet over a several month period may be more manageable. As well, it may be difficult to deal with a completely new diet if you make a dramatic overnight change. What to cook? What else can I eat? By making small consistent changes it might not seem so daunting.
Now, if somebody is suffering from some significant health issues, and they need to make drastic changes just to stay alive, then that may be plenty of impetus to get them to make a complete overhaul. Without the kind of shadow looming overhead, it might be difficult for some people to give up pleasure food and such.
Finally, when living with somebody who is not participating in this dietary change, it may be difficult to go "cold turkey" and institute broad sweeping changes. Grocery bills could go up dramatically if you are buying completely separate foods for several people. Getting the family on board could help this, but it may require gradual change for stubborn adopters.
The trick for me was to not worry about calories the first week, and eat whatever I wanted, when I wanted it, as long as it was primal. I found that it was easier to do without the grains and sugar if I had bacon, eggs, and avocado for breakfast, huge salads with nuts, oil, and berries for lunch, and steak, veggies, and a big bowl of fruit for dinner. I was probably over 3000 calories a day for that first week, but it worked wonders because I was always full so carb cravings were minimized! I still lost a few pounds, and once my body adjust I found myself eating less without thinking about it.
Since we (the husband and I) didn't have the cash to totally restock our kitchen and pantry all at once, we made the decision to stop buying SAD foods and use up what we had in the house while only buying paleo (non-SAD = happy?) foods from then on. That meant the canola and soybean oil have just recently been used up, but we've got a pretty solidly paleo kitchen now. I think it may have also helped us avoid cravings as the carb content of our diet dropped gradually as we used up the "old" foods. It didn't take as long as you might think, only a couple of weeks. At this point, there's a few SAD foods lurking in the freezer, but that's about it. (I'm making an exception for the edamame, as it is delicious, unprocessed and I grew it myself last summer.)
Once the transistion was done, it's been really easy to avoid temptation, as the icky stuff simply isn't there any more to be tempting!
I did it pretty much cold turkey. I was highly motivated to do so, though, due to a Type II diabetes diagnosis. Six weeks after I started my blood glucose levels were normal, which is one heck of a motivation to continue.
I would generally prefer a more gradual approch to any dietary change, however of course this varies depending on your personallity type and health. Trying to change diet, exercise and lifestyle all at once it quite a major change to undertake.
Choosing healthier foods for individual meals can be more of an interesting problem to solve as you find new recipes and foods to try. Then when you have a normal meal or snack you haven't failed in your diet, just find some more paleo food for your next meal. In this way healthy food gradually displaces unhealthy food from your diet rather than denying yourself everything your normally eat and then trying to fill the gap with unfamiliar food.
Tastes including things like for salt and sweetness change gradually over time. You learn to like more foods over time if you eat less sugar, fruits and vegetables taste sweeter. It is likely you will start to lose taste for some previous foods. There are many sweet fatty foods I just cannot stomach anymore.
Our intestines become adapted to our habitual way of eating, including factors like fibre and meal times. The commensual bacteria are also partly shaped by our diet. Abrupt changes in diet of any kind can cause issues.
It takes time to learn to shop for and cook new and possibly unfamiliar foods. This could be less stressful if done a little more gradually.
Focus on big factors at first, don't obsess about small details. Cutting out refined carbohydrates and sugar will have far greater impact than a bit of peanut butter.
In order to become a long-term change your lifestyle and good food has to become an interesting hobby that you enjoy.
The above are just my opinons.
You should do whatever feels easiest, whether it be cold turkey or one step at a time. I personally found it trivial to go cold turkey on bread, but I psychologically needed to know that I could eat sweets. As I read more and more and genuinely internalized what the sweets were doing to me, it became easier and easier to avoid them. But that's just me. You should so whatever you are most likely to stick with, whatever suits your particular psychology.