Welcome Tark!
PCGS and NGC are the two best known grading companies, but many people (including my sister and I) have had bad experiences with PCGS lately. I'm not sure how NGC compares.
For more you may want to read the PCGS thread here.
Also, keep in mind that few coins are actually worth grading. Grading is expensive -- a minimum of ~$25, up to $50 or more per coin, depending upon 'service level'; shipping & insurance costs; and how many coins are included in the submission.
In order for a coin to be considered for grading, the collector should be reasonably certain that the grading & holdering will pay for itself. That means that the coin should:
a) Have significant potential value. I say 'potential', because often a coin will appear to be right on the edge of a grade where it would be very valuable.
For example, you mentioned your 1881-S. Assuming it is "MS" and not "PL" or "DMPL" we see that it's value could be anywhere between $27 and $1,300:
http://www.PCGS.com/prices/pricegui...organ+dollar Let's say you think your Morgan is a MS63 ($60 retail value). In that case it probably isn't worth grading because even if it comes back as MS64 (doubtful, because most collectors over-estimate the grade of their coins) it would only be worth $15 more
OTOH, if your coin might realistically be, say, a MS65+ or 66 (or higher), then it's probably worth having it graded.
b) Vary significantly in value from one grade to the next. Many coins follow the same pattern as your 1881-S -- small steps in value in the lower grades, leading to large jumps in value at the highest grades. There are some though -- like many bullion coins -- that have essentially the same value up through MS/PR68, or even 69. In that case, it is not worth having the coin graded unless there is a strong possibility that it is truly a 70 (perfect) or at least 69.
Hope that is helpful.
BTW -- there are other well-regarded grading companies -- like ICG and ANACS. You might consider them.