"The Earth's sister planet revolves around our central star in an elliptical orbit that is the most circular of any planet. The difference between its aphelion (the orbital point farthest from the Sun) and perihelion (the orbital point where a body is closest to the Sun) is only 1.5 million km"
http://www.eso.org/public/outreach/eduoff/vt-2004/Background/Infol2/EIS-D3.html

"We make our closest approach to the Sun (147.5 million km) in January, that's called perihelion, and we're farthest from the Sun (152.6 million km) in July, that's aphelion."
http://science.nasa.gov/headlines/y2001/ast03jul_1.htm

So difference between Venus aphelion and perihelion is 1.5 million km, compared to Earth's difference of 152.6 - 147.5 = 5.1 million km. So in terms of traveling to Venus, Earth's larger difference should be more important than Venus's. Now, when leaving Earth, should it be done when Earth is nearest to the Sun {perihelion} or furthest away {aphelion}?

Which does NASA's choose [or is this not even considered very important}?
Which would you consider best?

It seems to me as general rule, whether going to an inner planet or outer planet leaving Earth at it's perihelion is a better time- though of course I realize there are many other factors involved. For instance just in terms of orbital eccentricity, Mars, has an even greater eccentricity: Mars is 0.093 {Earth: 0.0167 and Venus: 0.0068}.
http://www.solarviews.com/eng/homepage.htm

Earth's mean distance from the Sun is 149,600,000 km, and in terms of a circle, it's diameter 299,200,000 km with circumference of 939,963,728 km. If this is scaled down to a circle on piece paper, the Earth's orbit would appear to be a nearly perfect circle. And in the sense that whatever straight line has ever been made, seen or imagined by humans- Earth's orbital path [in actual scale] would be to be a straight line- not including that spacetime is curved by gravity- i.e., remove the affects of Sun's gravity and it is still straighter than any line or survey line ever made. Including the fact that spacetime is curved by gravity, Earth orbit not only appears to be a straight line because vast scale but would be an absolutely straight line if not for the slightly eccentric orbit.

I hope the above provides some context.

You could say Venus draws the most perfectly straight line and circle in our solar system, but as always, I'm wondering how to get somewhere. And in this occasion, specifically, what is the best way to get to Venus. Currently, one reason we go to to Venus is in order to get to Jupiter and beyond, and though we have not used Venus to go to Mars, it seems to me that this might be possible. It also seems more likely and probably more practical that one go to Venus in order to go to NEOs and other asteroids [such as Main belt].

Now, one thing against the idea of using Venus to go to Mars is it looks difficult and seemingly little benefits from doing so.
One could also make jokes about it:
"Abbott and Costello Go to Mars:
The film follows the misadventures of Lester and Orville who accidentally find themselves on a rocket destined for Mars which accidentally lands at the New Orleans Mardi Gras. During this visit they are forced by bank robbers Mugsy and Harry to fly to Venus where they encounter a civilization made up entirely of women."
http://en.wikipedia.org/wiki/Abbott_and_Costello_Go_to_Mars

Though it's not all fun and games:
Abstract:
"The analytical determination of launch dates and proposed trajectories is reviewed with respect to the search for a low-energy trajectory to Mars with gravitational assist from Venus for the years 1995-2024. Both Ballistic and Venus-Earth gravity assist (VEGA) trajectories are calculated with an automated design tool by the authors (1990). The trajectories are modeled as conic sections from one gravitating body to the next, and gravity assist is considered to act impulsively. VEGA trajectories to Mars require similar launch energies for 6 years listed and have moderate arrival C3s, with the lowest C3 requirement in 2015. The flight time and arrival energies of the trajectories are found to be larger than those of ballistic trajectories, but the low-energy launch window makes them desirable for unmanned Mars missions, in particular."
http://adsabs.harvard.edu/abs/1991JSpRo..28..486W

[btw, C-3 means capture or escape orbits]

"....Since this value of C3 corresponds
to a VM of 3.5 km/s, which is usually greater than the
V^ required for direct ballistic trajectories to Mars, higher
values of C3 were not considered. Note that Venus swingby
solutions appear only in 2015. In order to keep the flight times
as small as possible, all trajectory legs were restricted to less
than one revolution about the sun (type 1 and type 2 trajectories).
Several conclusions can be drawn from these figures. First,
the earliest year in which a VEGA trajectory has a lower
launch energy requirement than adjacent ballistics is in 2002.
There is a four-year gap between 2004 and 2008 in which neither
mission mode is available (C3 < 12.25 kmVs2). VEGA
trajectory launch C3s are clearly less than nearby ballistic opportunities
in several years (2002, 2008, 2010, 2020, 2021, and
2023). Also, in several years (2004, 2012, and 2015), VEGA
trajectories are comparable to nearby ballistics. In all cases,
VEGA trajectories offer an additional set of launch windows
that may be desirable for logistics reasons or for the purpose
of achieving different Mars arrival dates. Over the 30-year
span, the lowest ballistic launch energy occurred in 2018 (C3
= 7.75 kmVs2) and the lowest VEGA in 2010 (C3 = 7.59
kmVs2)."
http://pdf.aiaa.org/jaPreview/JSR/1991/PVJAPRE26270.pdf
[Old stuff: about 1990]

Now, what I wonder about is going to Venus via "Interplanetary Transport Network": http://www.answers.com/topic/interplanetary-transport-network

Now, Venus is nearest planet to Earth. And using Interplanetary Transport Network is least delta-v to get to Venus, but using least delta-v it is also slow. One thing I couldn't find a answer to was is there a speed limit on the "Interplanetary Transport Network"- could use more delta-v and still use it, or is it limited to low delta-v. Said differently could go through Earth/Sun L-1 at say +2 Km per sec and end up going through to Venus's Venus/Sun L-2.