Ukraine means 'in-land', 'native-land' and since the 16th century more commonly 'borderlands' and as a pivotal country in Europe, over the ages their borders and countries of influence have changed with parts of it for most of the time being a self ruled independent state. The formation of Ukraine as the Kievan Rus state started in 881 and grew until the 12th Century when it was the biggest state in Europe. All of the Rus states were ruled from Kiev so Ukraine actually existed before Russia did as a state. Ukraine is the mother of the Russian state, not the other way around like Putin likes to imply in his 'own version' of history for propaganda and annexation purposes.
Yes, the West part, West of the Dnieper river, has been part of Poland and at times other Western empires, which is why they are very Western looking. Putin's current war where the majority of Ukraine becomes part of the province New-Russia has not to date included this Western region as he has rightly concluded that trying to hold it against Ukrainian Partisan forces would make it too expensive in Russian lives. There is already considerable Partisan activity in the Donbass region and that will only get worse as Putin moves North and East.
The problem is that even if Putin annexes it the problem is not going to go away as there will be an Afghanistan situation in the heart of Europe. The much bigger danger is that to stay in power after most of Ukraine, and all of Moldova and Georgia are part of a Russian empire again, he will need need new enemies and wars. All of the immediate satellite '-stans' will work for a bit as he further expands his empire by taking them over to protect the 'Russian speaking populations', then he will be testing the water in the Baltics which are very difficult for NATO to defend, if they choose to do so. Personally, I don't think they will. Why would Aunty Merkel want to risk a war with Uncle Vlad to defend 3 very small countries?
The big advantage of backing Ukraine, with defensive weapons and financial help is that Ukraine as a non-NATO country is and will continue to do the fighting for the West and there won't be an infinitely more dangerous, direct NATO-Russian forces confrontation. So it is actually in the West's interests for Ukraine to do the fighting for them to a stalemate or even a partial victory. There two political reasons why this isn't happening: Obama / Rice long term global strategy that as long as you're nice to your enemies, eventually they will be as nice and dandy to you back, it is just going to take time. This resultant power-vacuum is why there is such horrendous global upheaval at the moment. With Europe it is all about their dependence on Russian gas, the biggest by far, by volume is Germany and Merkel is hoping, mistakenly IMO, the crocodile Putin will eat Germany last.
Poland has sensibly made the decision that they will need to fight Russia without US and NATO support and are modernizing and training to NATO standards and building up their military forces and civil defences up as fast as possible. Merkel has made it clear she is not interested in getting involved in any military conflict in any circumstances, East of the Oder river, which largely forms the German-Polish border.
One of the commitments of belonging to NATO is to spend 2% of GDP on defence. Only 4 countries do so: Estonia, Greece, UK and US. Germanies is 1.3% which is on the lower side of average for European countries. They expect like too many other European countries to have their collective defence on the cheap, with minimum spending and other NATO forces coming to the rescue if they get into trouble as a result.
Personally, I think the West is pinned its hopes on Putin falling due to a combination of economic sanctions and low oil price, if so it is an incredibly dangerous game as Putin has made it perfectly clear he intends to cling to power at whatever the cost, more strongly than a leech taking part in a bloodfest competition.
Putin allegedly killing 300 Muscovites by bombing apartment blocks to consolidate his power and as an excuse to start the Second Chechen war that killed over 300,000. This shows he will do whatever he has to do to anybody to stay in power. Any human life only has a slight worth to him if they are totally loyal and committed to work for his benefit, otherwise they are worth zero.
Unchecked, if he has to nuke a few billion people to stay in power he will do so and the danger of this will continue to grow as he gets bolder and consolidates his absolute position and authority as a ruthless Russian Dictator. More wise heads and sensible council are already ready gradually disappearing, replaced by more and more like minded flunkies, telling him what he wants to hear. The longer this continues the fewer sensible Kremin suits there will be around him to stop a human catastrophe.