Gdtyjr

I like the flexibility in editing afforded by custom inline enumitem lists; for example:

documentclassarticle
usepackageenumitem

newlistinlineitemitemize*1
setlist[inlineitem] % Customize itemize* environ
 before=unskip:, % Colon before list
 itemjoin=;, % Join with semicolons
 itemjoin*=; and, % Last join has "; and "
 label=, % No label
 after=. % Period at end of last item

begindocument

 Here is some text that will have a list of
 begininlineitem
 item a list item that could go first but also last
 item another list item that I'm not sure about
 item this one should go last unless I think of another one
 endinlineitem

 It's convenient because I can add, remove, and rearrange items without worrying about punctuation.

enddocument

I'd like to do the same thing with a non-inline list; however, enumitem's docs state that "itemjoin is ignored in vertical mode", and so it is.

Here's a possible solution that works by redefining item.
This may seem a little heavy-handed, but it is also how the itemjoin key for inline lists works.

I'm using SetEnumitemKey to define a new key, sentence, that can be supplied to any list environment that enumitem knows about.
It will append a period (.) to the last item and a semicolon (;) to every other item.

documentclassarticle

usepackageenumitem
SetEnumitemKeysentence%
 before*=sentencelistprep;,
 after*=unskip.,


letsentenceitemjoinempty
edefsentenceitemnoexpandsentenceitemjoinunexpandedexpandafteritem%
newcommand*sentencelistprep[1]%
 defsentenceitemjoindefsentenceitemjoinunskip#1%
 letitemsentenceitem


begindocument

Here is an textttitemize environment whose items are part of this sentence and therefore come with appropriate punctuation:
beginitemize[sentence]
item a list item that could go first but also last
item another list item that I'm not sure about that is long enough to span two lines
item this one should go last unless I think of another one
enditemize

It's convenient because I can add, remove, and rearrange items without worrying about punctuation.

enddocument

Warning: you can't use any other list environments inside one with the sentence key because the redefinition of item will also apply to those and will insert additional semicolons there as well.

(You probably wouldn't want to nest lists inside a running sentence, but if you have to you can add letsentenceitemjoinempty inside the inner list.)

Remarks

• I didn't include the colon (:) because does not feel like it is a part of the list (and not affected if items are reordered).
  If you do want the colon to automatically be inserted you can replace the value of before* above by unskip:sentencelistprep;.


• 
  

  If you don't want to have to supply the sentence key every time, you can create a custom list environment that includes it with e.g.

  
  
  

  newlistmyitemizeitemize1
  setlist[myitemize]label=textbullet,sentence
  

  
  



• The before and after keys overwrite sentence if supplied later, but the converse is not true because sentence uses the starred versions before* and after*.




• sentencelistprep;, which is called at the start of a list with sentence, does the following: it defines sentenceitemjoin asdefsentenceitemjoinunskip; and replaces item by a version that includes sentenceitemjoin.
  The first item therefore redefines sentenceitemjoin to unskip;, and every item after that consequently inserts a ; before it.

Addendum

Per your request, here is a way to add “and” to the semicolon in the penultimate item.
I couldn't do this by simply modifying the other solution because an items in a list environment can't really know if it is the final one.

The following works by first scanning the contents of the entire list environment and inserting ;s at the end of every item but the last one, and additionally adding and to the penultimate item. It's a little bit of a hack, but it works. (Unlike with the above version, you can nest another list environment in this one, though it still seems unlikely that you would want to.)

documentclassarticle

usepackageenumitem
usepackageenviron %% <- for Collect@Body

makeatletter %% <- make @ usable in command sequences
SetEnumitemKeysentence% %% <- register key
 before*=sentencelist@afterfi,

defsentencelist@afterfi#1fi %% <- insert sentencelist code after fi
 #1fiCollect@Bodysentencelist %% <- apply sentencelist to the body of the environment

defsentencelist#1@sentencelist#1item@sentencelist
def@sentencelist#1item#2@sentencelist
 #1@@sentencelist#2@@sentencelist %% <- just insert everything up to the first item

def@@sentencelist#1item#2@@sentencelist%
 ifrelaxdetokenize#2relax %% <- if last item
 if@newlistelse andfi %% <- insert "and" if not also the first item
 item #1unskip.% %% <- insert the item and a .
 else %% <- otherwise
 item #1unskip;% %% <- insert the item and a ;
 @@sentencelist#2@@sentencelist %% <- and repeat
 fi

makeatother %% <- revert @

begindocument

Here is an textttitemize environment whose items are part of this sentence and therefore come with appropriate punctuation:
beginitemize[sentence]
item a list item that could go first but also last
item another list item that I'm not sure about that is long enough to span two lines
item this one should go last unless I think of another one
enditemize

It's convenient because I can add, remove, and rearrange items without worrying about punctuation.

enddocument

Here is a version that sort of reproduces a display itemize allowing for the features of an itemize*. Below is the same content using inlineitem (provided in question), displayitem and a regular itemize for comparison purposes:

Notes:

• 
  

  The color red has been added to make it easier to compare the three versions. You can replace the definition of Show with

  
  
  

  newcommand*Show[1]#1
  

  
  
  

  to eliminate the highlighting or simply remove all references to the Show macro.

  
  



• The "sort of" is because I wasn't able to get the vertical spacing of the very first item to match what itemize yields.

Code:

documentclassarticle
usepackageenumitem
usepackagexcolor

newcommand*NextLine%
 newline
 vspace*0.5baselineskip%
 hspace*dimexprlabelindent+labelwidth-labelseprelax%
%
newcommand*Show[1]textcolorredbfseries#1% Make it easier to see difference



newlistinlineitemitemize*1
setlist[inlineitem] % Customize itemize* environ
 before=unskipShow:, % Colon before list
 itemjoin=Show;, % Join with semicolons
 itemjoin*=Show; and, % Last join has "; and "
 label=, % No label
 after=., % Period at end of last item


newlistdisplayitemitemize*1
setlist[displayitem] % Customize itemize* environ
 before=unskipShow:NextLine, % Colon before list
 itemjoin=Show;NextLine, % Join with semicolons
 itemjoin*=Show; andNextLine, % Last join has "; and "
 label=$bullet$, % Label
 after=unskipShow.endgrafnoindent, % Period at end of last item


pagecolorwhite
begindocument
 noindent
 Here is some text in a verb|inlineitem|
 begininlineitem
 item a list item that could go first but also last
 item another list item that I'm not sure about
 item this one should go last unless I think of another one
 endinlineitem
 Some text after verb|inlineitem|.

 bigskip

 noindent
 Here is the same text in a verb|displayitem|
 begindisplayitem
 item a list item that could go first but also last
 item another list item that I'm not sure about
 item this one should go last unless I think of another one
 enddisplayitem
 Some text after verb|displayitem|.

 bigskip

 noindent
 Here is the same text in an verb|itemize|
 beginitemize
 item a list item that could go first but also last
 item another list item that I'm not sure about
 item this one should go last unless I think of another one
 enditemize
 Some text after regular verb|itemize|.
enddocument