I would recommend against trying to reconstruct neanderthals however. There were probably real reasons why the neanderthal died out, and very likely requirements of modern life which the neanderthal was simply incapable of, and spoken speech could easily have been one such. A neanderthal trying to live in our world would not be happy.
This is one of Jay Matternes' reconstructions of a neanderthal:
And this is what some refer to as "non representational art" from the Indus Valley civilization, the so-called "priest/king" figurine:
Matternes had no way to know how much the brow ridges would show on a live subject and the jaw and forehead are identical. Somebody might have neglected to tell the artists of Mohenjo Daro or Harappa that neanderthals were supposed to have died out 40,000 years ago.
Then again, if you can read German, there is Gunnar Heinsohn's Wie Alt ist das Menschengeschlect in which Heinsohn, one of Europe's best scholars, claims that there is no legitimate reason based on stratigraphy or proper analyses of stratigraphical studies to think that neanderthals died out any more than about 3000 years ago.
Heinsohn notes (in English) that:
Mueller-Karpe, the first name in continental paleoanthropology, wrote thirty years ago on the two strata of homo erectus at Swanscombe/England: "A difference between the tools in the upper and in the lower stratum is not recognizable. (From a geological point of view it is uncertain if between the two strata there passed decades, centuries or millennia.)" (Handbuch der Vorgeschichte, Vol I, Munich 1966, p. 293).The outstanding scholar never returned to this hint that in reality there may have passed ten years where the textbooks enlist one thousand years. Yet, I tried to follow this thread. I went to the stratigraphies of the Old Stone Age which usually look as follows
modern man (homo sapiens sapiens)
Neanderthal man (homo sapiens neanderthalensis)
Homo erectus (invents fire and is considered the first intelligent man).
In my book "Wie alt ist das Menschengeschlecht?" [How Ancient is Man?], 1996, 2nd edition, I focused for Neanderthal man on his best preserved stratigraphy: Combe Grenal in France. Within 4 m of debris it exhibited 55 strata dated conventionally between -90,000 and -30,000. Roughly one millennium was thus assigned to some 7 cm of debris per stratum. Close scrutiny had revealed that most strata were only used in the summer. Thus, ca. one thousand summers were assigned to each stratum. If, however, the site lay idle in winter and spring one would have expected substratification. Ideally, one would look for one thousand substrata for the one thousand summers. Yet, not even two substrata were discovered in any of the strata. They themselves were the substrata in the 4 m stratigraphy. They, thus, were not good for 60,000 but only for 55 years.
I tested this assumption with the tool count. According to the Binfords' research--done on North American Indians--each tibal adult has at least five tool kits with some eight tools in each of them. At every time 800 tools existed in a band of 20 adults. Assuming that each tool lasted an entire generation (15 female years), Combe Grenals 4,000 generations in 60,000 years should have produced some 3.2 million tools. By going closer to the actual life time of flint tools tens of millions of tools would have to be expected for Combe Grenal. Ony 19,000 (nineteen thousand) remains of tools, however, were found by the excavators.
There seems to be no way out but to cut down the age of Neanderthal man at Combe Grenal from some 60,000 to some 60 years.
I applied the stratigraphical approach to the best caves in Europe for the entire time from Erectus to the Iron Age and reached at the following tentative chronology for intelligent man:
-600 onwards Iron Age
-900 onwards Bronze Age
-1400 beginning of modern man (homo sapiens sapiens)
-1500 beginning of Neanderthal man
between -2000 and -1600 beginning of Erectus.
Since Erectus only left the two poor strata like at Swanscombe or El-Castillo/Spain, he should actually not have lasted longer than Neanderthal-may be one average life expectancy. I will now not go into the mechanism of mutation. All I want to remind you of is the undisputed sequence of interstratification and monostratification in the master stratigraphies. This allows for one solution only: Parents of the former developmental stage of man lived together with their own offspring in the same cave stratum until they died out. They were not massacred as textbooks have it:
monostrat.: only modern man's tools
interstrat.: Neanderthal man's and modern man's tools side by side
monostrat.: only Neanderthal man's tools
interstrat.: Neanderthal man's and Erectus' tools side by side
monotstrat.: only Erectus tools (deepest stratum for intelligent man)
The year figures certainly sound bewildering. Yet, so far nobody came up with any stratigraphy justifiably demanding more time than I tentatively assigned to the age of intelligent man. I always remind my critiques that one millennium is an enormous time span--more than from William the Conqueror to today's Anglo-World. To add a millenium to human history should always go together with sufficient material remains to show for it.
Looking like us more or less, and being in any way interchangable with us are of course different things. The recent DNA studies have basically explained the big mystery of there being no evidence of cross breeding between us and neanderthals, and eliminated the neanderthal as a plausible ancestor for modern man and, all other hominids being FURTHER removed from us than the neanderthal, that leaves us with no plausible evolutionary antecedent for modern man on the planet and the idea of modern man having evolved, pretty much in tatters.