The Gemara (Shabbat 25a) states that there is a Mitzvah to bathe in hot water on Erev Shabbat. The Poskim tell us that even a Torah scholar whose Torah is his livelihood should take some time off from his learning to bathe on Friday afternoon in order to enter Shabbat pleasantly and with cleanliness. One should nevertheless take care not to take a shower too close to Shabbat so as not to, G-d forbid, desecrate the Shabbat and also so as not to enter Shabbat pressured and in a rush.
Preferably, one should shower specifically on Friday and not on Thursday, so it is noticeable that he is showering to honor the Shabbat. Nevertheless, the Mordechi writes that one who cannot bathe on Friday for whatever reason may do so on Thursday night or even on Thursday during the day and the closer it is to Shabbat, the more noticeable it is that one is bathing in honor of Shabbat. Several great Acharonim, including the Bayit Chadash and Maran Ha’Chida, quote this opinion. It can be understood then that one whose hot water tank is heated using solar energy and the like (common in Israel) and there will not be enough hot water for the entire family to shower on Friday, the children may be bathed on Thursday and the adults should shower on Friday.
The same Halacha would apply regarding a haircut, in that one whose hair is long and is already planning on taking a haircut, there is a Mitzvah for one to do so as close to Shabbat as possible. Similarly, one who regularly trims one’s beard should do so as close to Shabbat as possible. If one is unable to take a haircut or trim one’s beard on Friday, one should do so on Thursday. The same applies to cutting one’s nails, in that there is a Mitzvah to do so on Friday in honor of Shabbat.
Regarding cutting one’s nails, the Rama quotes in the name of the Abudirhem that one should not cut one’s finger nails in order, for there is a danger in doing so. Rather, one should cut them in the following order: On one’s left hand, one should first cut the nail of his ring finger, then the index finger, then the pinky, then the middle finger, and finally, the thumb. On one’s right hand, one should begin by cutting the nail of the index finger, then the ring finger, then the thumb, then the middle finger, and finally, the pinky. Many Poskim have ruled this way as well, at least preferably.
However, the Halacha on this matter follows the ruling of Maran Ha’Chida who writes that Rabbeinu Ha’Ari z”l, to whom all the secrets of the Torah were revealed, was not careful about this matter and would cut his fingernails in order, one after another. Additionally, the Ari z”l would cut the nails of his fingers and toes on the same day, even though there are others who recommend not doing so because of the danger involved. Therefore, if the Ari z”l was not cautious about these matters, surely there must not be any danger involved. Therefore, it is our custom that one cuts one’s nails in order, one after another, and one may also cut one’s fingernails and toenails on the same day.
Summary: There is a Mitzvah for one to wash one’s self with hot water on Erev Shabbat. This washing should preferably be done as close to Shabbat as possible, i.e. on Friday. However, if one is unable to shower on Friday, one should do so on Thursday night or Thursday during the day. There is also a Mitzvah to take a haircut or trim, when necessary, on Friday. Additionally, there is a Mitzvah to cut one’s nails on Friday as well. Our custom is that one cuts one’s fingernails in order, one after another, and we are not worried about the warning not to, as is written in several holy books.