I have an existing power receptacle and wiring whe

a) power comes into the bottom outlet
b) additional receptacles are daisy chained off the bottom outlet
c) the top plug is switched... an additional hot line comes off the
bottom outlet, goes to the switch, and then goes to the top
outlet.

Everything works OK. However, when I went to replace the
receptacle with a new and different colored one I noticed the
wiring and started to wonder about something. Bear with me,
for this is hard to ask without a diagram...

Lets name the power feed wires coming into the bottom outlet
HOTin and NEUTRALin. Lets name the wires that feed the
other receptacles HOTout and NEUTRALout. Lets name the
switch wires SWITCHin and SWITCHout. The receptacles
I'm working with have screw terminals and corresponding push
in type terminals. So there are options in terms of how the wires
are connected. For example, HOTin could be pushed in and
HOTout could be connected to the corresponding screw terminal.
Or vice versa. Or both could be connected to the screw terminal.
Etc.

As it stands right now... HOTin and NEUTRALin are connected
to the lower outlet's push in terminals, HOTout and NEUTRALout
are connected to the lower outlet's screw terminals, and SWITCHout
is also connected to the lower outlet's screw terminal. What I got to
wondering about is whether there is a "proper" way to make such
connections and whether what I have is it. Or whether it really matters.
IOW, is it OK that power comes in via push in terminals and goes out
to other receptacles via corresponding screw terminals? Or should
it be the other way around? Or should both in and out be connected
to the screw terminals?

Hope you follow what I'm asking ;-) Thanks in advance for an info.