There are no objective best starting spots. Too much depends on map settings, opponent and preferred strategy.

it depends.

1vs1, then I think to start in teeritories belonging to the small bonuses is best example small earth to start in Austrila and have one in SA to the border of Africa (or vice versa), and one in NA at the border to Europe (or vice versa). Taking control over Australia would be much eaiser then taking control over Asia (and also much faster). With standard settings (no cards) this would give you 5+2armies each turn, then you will be able to take SA (5+2+2 armies/turn(s)). If you still have armies in in Greenland or Iceland your opponent can then only control Africa (assuming you have armies in Siam). This means that you will receive 9 armies and your opponent max 8. Then you should take control over Africa and at the same time NA (if the opponent is only receives 5 armies).

However, looking at a big map with many territories such as the US map with 3.1K territories it depends on your strategy and where your opponent start.

to realize all possible 4 spots you pick, you pick all combinations from the 3 spots and analize the possible locations of last picks.

For example, if you pick your 123 as your 3 initial picks, is very easy to understand that you can get all other 5 picks as the last one.
1234
1235
1236
1237
1238
being all possible. From there on you can do the proper table. Tired to do it, but is not hard at all.

And Kerostar statement is completely accurate and usefull, and putting that knowledge in picking can do wonders.

For 1v1 with 4 starting spots the possibilities are:
1234
1235
1236
1237
1238
1245
1246
1247
1248
1256
1257
1258
1267
1345
1346
1347
1348
1356
1357
1358
1367
1368
1456
1457
1458
2345
2346
2347
2356
2357
2367

JSAs list was extremely close.

Some combinations require you to get either 1st or 2nd pick, others are always possible, regardless of 1st/2nd pick. These latter ones are twice as likely.

1v1, 3 spots:
123 1st/2nd
124 1st/2nd
125 1st/2nd
126 2nd
134 1st/2nd
135 1st
136 2nd
145 1st
234 2nd
235 2nd
236 2nd

1v1, 4 spots:
1234 1st/2nd
1235 1st/2nd
1236 1st/2nd
1237 1st/2nd
1238 1st
1245 1st/2nd
1246 1st/2nd
1247 1st/2nd
1248 1st
1256 1st/2nd
1257 1st/2nd
1258 1st
1267 1st/2nd
1345 1st/2nd
1346 1st/2nd
1347 1st/2nd
1348 1st
1356 1st/2nd
1357 1st/2nd
1358 1st
1367 2nd
1368 2nd
1456 1st/2nd
1457 1st/2nd
1458 1st
2345 2nd
2346 2nd
2347 2nd
2356 2nd
2357 2nd
2367 2nd

Statistical probabilities are rather pointless though, since the outcome is influenced much stronger by other factors (total number of starting spots in distribution, wastelands/bonus size/expansion options -> starting spots not being equal, strategy (single, double, triple pick, large/small bonus etc.), personal preference).
Lucky for you, I like numbers and am really, really bored right now, so here are the probabilities for 1v1, 2 picks.
1st column = pick / combination of picks
1st row = number of territories in distribution / number of territories you want to consider elegible (= non wastelanded bonus, no 3/4-turns-to-complete for example)
Percentages = probability of getting exactly that pick / combination of picks.

	6	8	10	12	14	16	18	20	22
1	80,9%	84,3%	86,9%	88,7%	90,2%	91,3%	92,2%	92,9%	93,5%
2	63,0%	69,0%	73,9%	77,6%	80,4%	82,6%	84,4%	85,8%	87,1%
3	55,3%	64,8%	71,3%	75,8%	79,1%	81,7%	83,6%	85,2%	86,6%
4	59,0%	59,9%	54,5%	48,8%	43,8%	39,5%	35,9%	32,9%	30,3%
5	38,5%	20,9%	13,0%	8,8%	6,4%	4,8%	3,8%	3,0%	2,5%
6	3,4%	1,1%	0,5%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%
									
									
	6	8	10	12	14	16	18	20	22
12	43,9%	53,3%	60,7%	66,3%	70,6%	73,9%	76,6%	78,8%	80,6%
13	36,2%	49,1%	58,1%	64,6%	69,3%	73,0%	75,8%	78,2%	80,1%
23	25,9%	38,0%	47,8%	55,1%	60,8%	65,2%	68,8%	71,7%	74,1%
14	48,7%	48,7%	44,1%	39,4%	35,3%	31,8%	28,9%	26,5%	24,4%
24	30,8%	33,4%	31,1%	28,2%	25,5%	23,1%	21,1%	19,4%	17,9%
34	30,8%	33,4%	31,1%	28,2%	25,5%	23,1%	21,1%	19,4%	17,9%
15	30,8%	16,7%	10,4%	7,1%	5,1%	3,9%	3,0%	2,4%	2,0%
25	23,1%	12,5%	7,8%	5,3%	3,8%	2,9%	2,3%	1,8%	1,5%
35	15,4%	8,4%	5,2%	3,5%	2,5%	1,9%	1,5%	1,2%	1,0%
45	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
16	2,3%	0,7%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%
26	2,3%	0,7%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%
36	2,3%	0,7%	0,3%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%
									
									
	6	8	10	12	14	16	18	20	22
123	6,8%	22,3%	34,6%	43,9%	51,0%	56,5%	61,0%	64,6%	67,6%
124	20,5%	22,3%	20,8%	18,8%	17,0%	15,4%	14,1%	12,9%	11,9%
125	15,4%	8,4%	5,2%	3,5%	2,5%	1,9%	1,5%	1,2%	1,0%
126	1,1%	0,4%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%	0,0%
134	20,5%	22,3%	20,8%	18,8%	17,0%	15,4%	14,1%	12,9%	11,9%
135	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
136	1,1%	0,4%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%	0,0%
145	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
234	10,3%	11,1%	10,4%	9,4%	8,5%	7,7%	7,0%	6,5%	6,0%
235	7,7%	4,2%	2,6%	1,8%	1,3%	1,0%	0,8%	0,6%	0,5%
236	1,1%	0,4%	0,2%	0,1%	0,1%	0,0%	0,0%	0,0%	0,0%

I don't really claim these numbers to be 100% correct, so please prove me wrong. Which might be difficult though, because I am too lazy to explain my calculations to you ;-)