Yup, is the correct book.
Not the most well-written, but a bit better than I recall.
Characterization of Our Hero is pretty wooden. Much old-school stuff (author was born in 1927), like formal Gaelic welcoming of the clan-leaders to do funeral stuff. Attempt at modernization (1 and 5 year marriage contracts), but mostly dated stuff going on (skirts and kilts going to zero-g, gee those crazy women can’t dress correctly).
About zero mention of saving anything other than cows, sheep, and humans - for your ecological considerations 
Lots of (semi-realistic) detail about some things - then meshed with magic technology: like melters which make any rock into lava and/or vaporized away. Orbital maneuvering is complex… but we don’t need a computer to do it in an alien ship; whose language and controls we don’t understand.
Our deductions are infallible!
Etc.
Analog review on the front says: ‘…should please every reader who see “Doc” Smith as an embodiment of SF’s Golden Age.’
As the blips rising from Pluto’s surface appeared on the repeater screens, Major Duncan Campbell of the Argyll and Sutherland regiment could see that the United Nations scouting force was outnumbered six to one by the mysterious aliens who’d materialized from nowhere to destroy the Plutonian base. Six to one: impossible odds, but it wasn’t in the Highland spirit to shirk… and perhaps the Sampson, the Minotaur and the Ajax could weaken the enemy before the inevitable defeat.
But when the Sampson’s computers began the gut-wrenching evasive maneuvers of deep-space dogfighting and her weapons systems sprang into action, the odds changed quickly. One after another, the alien warships were blasted into drifting debris; it was clear that the enemy was accustomed to another style of fighting.
All at once, the surviving attackers vanished, leaving the bewildered Scots in possession of the battlefield but uneasily aware that they faced an enemy with a superior technology. No human ship could simply disappear. And it was only a matter of time before the unidentified fleet returned, upgunned and with new tactics, to finish the task of destruction begun on Pluto.
It was up to Campbell, his crew and thousands more like them to find some way to avert the hammerblow they knew would come, to find some chink in the enemy defenses, to find some route along which to carry the war to an unknown planet in an unmapped star system… before the war was brought to Earth.
Human tech:
Tapes hold all messages, but multiple redundant computer systems exist 
Ship assembly happens at the bottom of Earth’s gravity well (dumb, esp. because author moves to space-based construction later).
Steam-jet manuveuring drives for ships.
Going major fractional C is not a major problem - even for huge asteroids, some shielding barely mentioned.
Apparently infinite power from something (reactor rooms)?
Magic transuranic element 126, celaenium. Also used in warheads; 37mm machine rocket rounds contain two 72g hemispheres separated by a thin lead membrane with proximity-fused rounds that can be set to different sensitivity raidii.
Any element can be synthesized in the cryogenics section.
Alien tech:
The hyperdrive doesn’t work much inside of the range of Pluto.
p6 lays out the political situation:
Blocs pulled out of the UN some time ago - the situation has been unstable for decades:
Major blocs are: US + clients (American Birch Bark Society / America First Party; a one-party system w/fundamentalists == “You just want back on America’s dole, we shan’t be lured into involvement with your petty tricks and lies.”), China (Chinese Presidium / People’s Celestial Republic == “You foreign barbarian dogs, our Malay half-breed translators will degrade themselves to speak your filthy tongue.”), Russia (but really == USSR) + clients (Soviet Foreign Minister == “You capitalist swine!”), EU (EU Minister / “We’re the only bastian of Civilization!”)
UN = 40 small countries + UK == the garbage can of the big blocs. Assigned Antartica, because otherwise blocs would occupy and fight over it, each having to fortify and defend otherwise useless territory - or worry what others were doing with it, etc.
Same in space with an informal agreement with the Blocs a decade ago; UN got Mercury and Pluto, and kept two Moon bases - signing over all claims on Luna, Mars (being settled now) and Venus (in the process of being terraformed; water pulled out of clouds) to the blocs. Other chunks are still up for grabs in the solar system.
First round; UN responds to Pluto base getting razed with 3 ships (one a utility vessel, headed by our Hero) vs. 23 alien ships.
Political stuff; no bloc believes in alien threat, but UN announces massive shipbuilding program, all other blocs follow suit, in order to maintain balance of power in case UN aligns with one of them against the others.
pg.52
“The High Command feels the original assault of Pluto was largely accidental. An enemy approaching from the opposite quadrant would never even notice Pluto since it would be some six thousand million miles distant and on the opposite side of the sun. And even had they broken out of their space drive just thirty to forty degrees on either side of her 'twould be unlikely they would have altered course simple to investigate a frozen ball of ice and metal far off on their flank. To the High Command’s way of thinking this indicates the enemy must have broken out of their hyperdrive somewhere in the immediate vicinity of Pluto, detected the base on their electromagnetic devices and attacked.”
Humans get a fairly long time to prep, shipbuilding, idea for asteroids as forward base(s) for logistics/supply, military training for vast expansion.
Round two; Humans conclude aliens will seek battle at fairly even odds, in order to test out improvements - turns into 1415 vs. ~500 human ships, in a running battle, UN does much of the fighting (but other blocs back them up after being engineered to be in the way by the UN), only 200 alien ships escape.
Afterward, blocs refuse to unite to save Earth. UN announces major mobile asteroid base building program, blocs consider following suit.
Round three; FTL used inside Pluto-limit, to take bombs to center of the Sun to cause it to go Nova or flare - happens pretty quickly, some people make it off Earth, but many of the survivors were already enroute.
Survivors are the ones who made it past Jupiter’s orbit, and thus survive the Sun swallowing everything else (and blowing off most of Jupiter’s atmosphere): 110K Americans (but 2/3rds male - stupid Americans), 35K English, 20K Indians, 60K Japanese, 72K Russians, 22K Africans, 9K Jews, 51K Arabs and Persians, 5K Chinese (49/50ths female) - total ends up with ~550K human survivors, the bulk of which are Scots.
Scots and UN rally on Styx, build last ship:
Revenge ship: ‘Claymore’, outfitted with 4K torpedo launchers and 4K warheads of 50 kilomegaton rating (200 == obliterate a continent), over 11K 44mm machine cannon. 3 celaenium-producing facilities. 22sq miles of surface area studded with bewildering arrray of defenses and special devices. 5K humans.
Send it off, getting up near C towards alien’s base detected by sensor-net when aliens did round three… which turns out to be their homeplanet (humans name it Shiva)
Aliens don’t seriously investigate Sol system until 20yrs later, while Claymore is enroute (and detects them passing them by).
Clandestine effort to secure the hyperdrive, and send back info to human survivors on Styx, then Attack!
Aliens have a 12 system empire, and like to torture aliens they take over, who they don’t consider real/sapient.
All alien ships, including those without hyperdrive, apparently carry the plans for hyperdrive in a manual, so humans win!
Attack: One pass, asteroid with only a few support ships (Danish?), takes on 1,200 alien vessels, carpet-nukes Shiva to the radioactive-slag stage.
Claymore heavily damaged, begins repairs, and slags several attempts to follow it. Goes 500ly away from Earth, and 400ly from Shiva, and plops down on a planet, newly named: New Skye
Nobody else has ever said that, so sometimes I felt like I was from an alternate Earth…