May one read a newspaper?
Newspapers which contain matters relating to business, economy, and advertisements, are forbidden to be read, even with intent to read only the non-business related sections and articles, being that it is very difficult for one to prevent oneself from reading the other sections. However there are some Poskim which permit reading the news sections, so long as one does not read the business sections. However even to them it is proper for every G-d fearing Jew to avoid reading newspapers on Shabbos.
Newspapers which do not contain any business related matters: Are permitted to be read, although one is to avoid doing so as many times the articles contain content which cause one to be saddened, which is forbidden on Shabbos.
News papers with pages designated for words of Torah and other pages designated for business: It is permitted to read the Torah sections, although some are stringent to require one to only read them in his mind, without verbalization.
Magazines and newspapers with advertisements: Seemingly advertisements have the status of business related matters. However this matter requires further clarification as the world is accustomed to be lenient to read pamphlets and magazines etc which contain advertisements, despite the above accepted ruling not to read papers which contain business related matters.
May one read the captions under the pictures in a newspapers or magazine? Seemingly this is forbidden, as explained above in Halacha 7, however the world is lenient to do so.
Are newspapers which are forbidden to be read Muktzah? They are MM”I, and if they are forbidden to be read even during the week due to them containing matters of heresy and promiscuity, then they are MM”G.
May one order newspapers from the company if they will also be printed and delivered on Shabbos on his behalf? No. It is strictly forbidden to allow the newspapers to be delivered for him on Shabbos as the gentile is transgressing a prohibition on behalf of the Jew in delivering it. This is aside for the fact that the printing press is printing an extra newspaper on Shabbos on his behalf. [It is however permitted for one to order a daily paper from the company telling them that he is not interested in receiving any newspapers on Shabbos or holidays. In such a case, even if the company chooses to still send the newspapers, this has no Halachic impact for the Jew.]
Are newspapers which are forbidden to be read Muktzah? 
They are MM”I, and if they are forbidden to be read even during the week due to them containing matters of heresy and promiscuity, then they are MM”G.
 Piskeiy Teshuvos 307/9
 Yaavetz 162; Ketzos Hashulchan 107 footnote 53, Mishneh Berurah 307/63.
 SSH”K 29/46; Beir Moshe 6/66 allows reading them in the bathroom. The Shevus Yaakov is lenient and rules that it is permitted to read newspapers.
 Reading news is not within the category of words of vanity as there is necessity to know the news items, as well as that one receives pleasure from the reading, and it is painful to refrain one from doing so. [Yaavetz ibid, brought in Ketzos Hashulchan ibid]
 Ketzos Hashulchan ibid
 SSH”K 29/46 based on Daas Torah 307/14, there they permit reading articles of Torah in all cases [implies even on same page as business related matters.]
 Az Nidbaru 9/7
 So is implied from term used by Yaavatz, and so seems logical. So is implied also from SSH”K ibid
 See Piskeiy Teshuvos 307 footnote 42. The Magen Avraham 301/4 allows to read captions written under pictures for the sake of pleasure. However other Poskim argue on this. [See Beir Moshe ibid, and Ketzos Hashulchan 107/2 how he learns this Halacha.]
 Beir Moshe 6/66
 Beir Moshe 6/66, based on Teshuvos Mahrahm Shick 123
 Mahrahm Shick ibid.
 Beir Moshe 6/66