OK I have chance to catch up now :o
Fair warning - not wishing to be a doom monger but it is fairly common for sleep to be decent at this age and then suddenly all go to pot at 4 months old. Just to say that it's nothing you've done if this happens!
Yes defo buy Christmas/birthday presents early and squirrel them away. Having all the birthdays in the second half of the year makes that a bit tricky here. But what is good about that is that if there's anything I missed for birthdays, or they get sets for their birthdays, we can do add ons to that for Christmases. I do a lot of second hand as well. And TK Maxx can be really good for toys and books if you have one. Christmas for a 4 month old is just a normal day for them really. For DS1's first Christmas we got most of his presents in the sales. DS2 got a set of dribble bibs (these are the kind you need for this age BTW) and some clothes in the next size up and some books for when he was older. For both of them I got them a jumperoo type thing as their "main" present. DS2 also got a flashing lights and sounds toy arch, which turned out to be brilliant as he liked lying under it at that age, later batting at the toys, when he could sit up pressing the buttons and then it came in handy as a nappy changing distraction until he was about 1 and lost interest!
I think Alex is refluxy as well but it's not really causing a problem for us so I'm not keen to give medication etc.
I think UK vaccinations are at 8 / 12 / 16 weeks. Here in Germany they get Rotavirus vaccine as well which is oral. That is supposed to be given at 6 weeks but we haven't had it yet. His next appointment is at 4 months and so if it is like it was for DS2 then they will do them at 4/5/6 months with the Rotavirus being done with the first one. My take from this is that it's not necessarily as urgent as it seems. Yes chicken pox is standard but it's given with the MMR at 1 year old.
I am not a fan of dungarees or trousers for this age though I do think dungs look cute and have a few. Sleepsuits are just easy and cute. But really hard to find in Germany... here the favoured newborn outfit is a long sleeved vest and "strampler" which is a kind of dungarees but maddeningly with no poppers at the bum! I mean WTF is that all about? I hate them.
We have accumulated a lot of blankets over 3 babies... I tend to just use the same one to cover him at the moment in the car seat/pram/etc - he can't be in both at the same time so I just move him and the blanket. Then I chuck it in the wash if he's sick on it. Agree those car seat blankets tend to affect the fit of the straps no matter how safe they supposedly are. I don't like them. We have inherited a Phil & Ted's buggy from a friend so I've put a fleecy footmuff in the bottom lie flat bit to make it cosy and contained. I find a footmuff works well in any buggy seat with straps, however early they go into one. The footmuffs that are sold for car seats tend to work well in a carrycot because they're small and good for babies up to 6 months or so, as an alternative to a pram suit.
The one copper popper! It's something that's new to me but all my new ones this time have it. Next and Primark. Apparently it's to match up to prevent you getting confused. Probably a good idea but I have got used to how to do it now without that. Baby Gap quality is gorgeous but the sizing is odd. We have a 6-12 month sleepsuit that is really more like 3-6 months particularly in the width, but a knitted cardy in 0-3 which lasted him until he was nearly 1! Their vests are true to size. I think the reason John Lewis is inconsistent is they have several brands.
Agree there is no sense in rigidly following any set "parenting style". I think it can be really helpful to look at what you want to achieve and/or what you want to avoid and start there, rather than starting with solutions and working backwards. So for example you said you want to enjoy this time and you want to establish a routine. To me, establishing a routine is not a problem or goal, it's a solution or a route to a goal. That goal might be predictability, or more sleep, or easier sharing, or it might be something else. So it may help to step backwards and think about what you're hoping the routine will achieve, and then you can look at that aim in conjunction with "enjoying the baby stage" (whatever that looks like for you) and your DH's "not being too attached" (I don't believe there is any such thing personally! But it's helpful to try and quantify what this means and how this might look for you two) once you have all the goals in view then it becomes easier to work out an approach which hits all of them.
Of course that in itself is all very complicated and you might just be too tired - in which case I would focus on survival right now rather than worrying about any time in the future, and when you have a bit more brain space, go back to the convo about what our parenting should look like.