What makes a good start to a paragraph is how it links in with the previous paragraph. What you require is a flow, a series of effortless transitions between the points you are making. Not only will this make your document easier to read but will strengthen any arguments are making.
This is because well executed transitional words between paragraphs help to spell to the reader a sound mind, organised thoughts, logicality and connectedness of ideas.
To summarise the previous paragraph of status:
After all, all in all, all things considered, in any case, in any event, in conclusion, on the whole, in short, in summary, in the final analysis, in the long run, on balance, to sum up, to summarise, finally.
If you're maintaining a sequence:
First of all, to begin with, in the first place, at the same time, in time, in turn, later on, meanwhile, next, then, soon, the meantime, later, while, earlier, simultaneously, afterward, in conclusion, with this in mind.
If you're restating what went before:
Namely, in brief, to put it differently, in essence, in other words.
If you wish to express similarity between points try:
In comparison, coupled with, correspondingly, identically, likewise, similar, moreover, together with.
If you wish to illustrate a particular aspect:
For example, for instance, for one thing, as an illustration, in this case.
If you are generalising:
Ordinarily, usually, as a rule, as usual, for the most part, generally, generally speaking.
For exemplifying and emphasis:
Particularly, especially, for instance, above all, chiefly, in particular, singularly, including, specifically, chiefly, markedly, namely, with attention to.
For making an exception try:
Except, excepting, excluding, aside from, barring, beside, exclusive of.
For a slight diversion or an aside go for:
By the way or incidentally.
For the classic device that is compare and contrast use:
Yet, however, still, nevertheless, on one hand, on the other hand, on the contrary, rather, contrast this, by the same token, conversely, instead, likewise, in contrast.
To display a consequence:
Hence, otherwise, therefore, as a result, consequently, for this reason, thus, thereupon, wherefore, subsequently, accordingly, for this purpose.
While for simple addition:
Also, again, as well as, besides, coupled with, furthermore, in addition, likewise, moreover, similarly.