starting with ODIs is better. in this era without warm-up matches it gives players time to get used to conditions, it also sets up the rivalries for the tests.
if they have to had an ODI series (which I really don't think they do) then it's better before.
I preferred it when ODIs preceded Tests, but I guess some of it in England might be down to nights closing in, changes of weather etc. In an ODI you can alter the parameters, change it from 50 overs to say 25 overs a side whereas in Tests it is time lost, attempted to be made up but can be simply lost and the game drifts towards a draw.
ODIs are already established under lights mind, if they try floodlit Tests then there is no reason the schedules can't be switched.
The reason I like ODIs before Tests is it is a warm up for the main event, gives the two sides a chance to hit form against decent bowlers in a competitive match rather than what counties/state/provinces/representative XIs offer. You can also try out players who might be aimed at playing ODIs but could also do a job in Tests, while the formats may have different demands, you still have the same basics and quality of batting/bowling.
Here's a few who debuted in ODIs before Tests, I picked Caddick, Gough and Cork because they were our best bowlers along with Gus Fraser and made Test debuts in 93, 94 and 95 respectively yet perhaps didn't all play together as much as they could have (37 times if memory serves, notably the first time we beat West Indies in a long time in 2000)
DEBUTS
Ian Botham : ODI = August 1976, Test = July 1977
Allan Lamb : ODI = 2nd June 1982, Test = 10th June 1982
Alec Stewart : ODI = October 1989, Test = February 1990
Martin Bicknell : ODI = December 1990, Test = July 1993
Dominic Cork : ODI = August 1992, Test = June 1995
Andrew Caddick : ODI = May 1993, Test = June 1993
Darren Gough : ODI = May 1994, Test = June 1994
Marcus Trescothick : ODI = July 2000, Test = August 2000
Andrew Strauss : ODI = November 2003, Test = May 2004
Beats me why Bicknell was dropped from ODIs, he averaged mid-20s with bat and ball. These days there is more a leaning towards specialists for ODIs and Tests, personally my view is that anyone who is quality should be able to play both. One exception maybe for me is Neil Fairbrother who should make the England best ever ODI XI but averaged a poor 15.64 from 10 Tests
NH Fairbrother (matches in brackets)
Tests (10) : 219 runs @ 15.64 (HS 83)
ODIs (75) : 2092 runs @ 39.47 (HS 113)
World Cup (19) : 430 runs @ 43.00 (HS 75no)
His 62 in the 1992 World Cup final very nearly pulled England out of the fire, from 69/4 to 180/7 when he finally got out. Those were the days when no World Cup final had been won by the side batting second.