How to allocate funds?

[Special T]

I will echo what other have said. #1 boots. Very subjective and worth every penny you spend. I personally would buy from some one whom is both a cobbler and a shoe salesman. If you are like lots of people you do not have perfect feet or gate and the right boots make all the difference in the world.
#2 pack also an area where fitment is important. If you have owned a few and are aware of how to best fit one I would suggest trying a USMC military surplus internal frame pack. My brother and I have lots of hiking experience and he picked one up with the assault day pack for under $200 that was is awesome shape. There may be better packs out there but I think this is a great bang for the buck back pack. #3 sleep system. I've always been a fan of a sleeping bag, a bevy sack and a light weight tarp. I used an Outdoor Research bivi similar to thier Heilum for 2 months. To me it was the perfect combination of tent light weight for backpacking. I used it for weekend, week-long trips as well as when I guided for the Boy Scouts for one whole summer.

I have also been a fan of hammocks because they are comfortable but they dont work everywhere and are not as warm.

[Fl0und3rz]

If you have owned a few and are aware of how to best fit one I would suggest trying a USMC military surplus internal frame pack. My brother and I have lots of hiking experience and he picked one up with the assault day pack for under $200 that was is awesome shape.

Seconded.  I picked up the USMC ILBE gen 2 here and purchased an assault pack separately.  Still only out $180, designed by ArcTeryx, made by Propper, and it was essentially new.

[DOUBLELUNG]

I put more importance on boots than pack, but not much.  so boots, pack, sleeping bag.   for me   

Agree!  Start at the trailhead, what do you need?  Boots, clothes, hydration system.  Pack.  Food/cookwear.  chair/seat.  Sleep system.  Another way to approach - what do I need for an hour? a day? an overnight?  Two nights?  5 nights?  Up to whatever max time you think you'd spend out before resupplying.

[kselkhunter]

This would be my priority of funds if starting backcountry hunting new:
1.  Boots - a quality pair of boots is the most important item for me.  I tried the cheap options for many years and had to replace every few years, then after prompting from a buddy of mine from Alaska went to the Zamberlain brand.  Never looked back.  Mine are 5 years old and still going solid.  Get the full leather option and use sno-seal every year, and they'll last a long time.  Buy new.
2.  Pack.  Any of the quality pack manufacturers make great options.  Pick what you like, and look for a used deal.  Kifaru, Mystery Ranch, Stone Glacier, Eberlestock, Kuiu, etc. all make good stuff.  I pack a Kuiu on lighter trips for deer, and Mystery Ranch for elk and longer trips.
3.  Tent.  Figure out what you like.  Tarp, Floorless, Floored, etc.  Whether you're going solo or with friends.  Etc.  Far too many options to list.  Lots of used options here on the forums.  My favorite floored model is Big Agnes, and floorless I prefer the Seek Outside tipis (which you can also buy an inner room for if you want part of it floored with bug screen).
4. Water filtration.  Depends on preferences and how long you're out, and how big your group is.  For solo I like the Sweetwater Guardian for it's pumping speed.  For group trips nothing beats the Katadyn Base Camp option.  Just dip the bag in the creek and hang it at camp. 
5.  First Aid kit.  Whatever your preferences are for level of coverage vs. weight tradeoff.
6.  Sleeping bag.  Far too many options to list.  And lots of opinions of down vs. synthetic fill.  Buy new.  I like my Feathered Friends down bag.
7.  Pad.  Go light.  Try to find used if possible, but not too expensive new.  I use ThermaRest NeoAir.  Sometimes pack the thermarest ultralight cot if it's a full week.
8.  Cooking items.  Personal preferences will drive your selection here.  I use the JetBoil system.  Sometimes pack the fry pan top they offer and some frozen meat to eat the first night or two before living off Mountain House meals the rest of the trip. 
 

[follow maggie]

For me, everything comes behind good boots & staying dry & warm

[T-Dozzer]

Boots, pack, sleep system. After that, we're arguing nuances.

[swanny]

Yep, get your main/heavy gear out of the way first (pack, tent, sleeping bag, sleeping mat). I'm going to assume you already have boots, but maybe I missed where you said you need those.

If you aren't going solo, I would scratch the tent from your list from the time being. Chances are your buddy has one already and it's much lighter for the team to carry one tent than to each carry your own. Also will provide much easier time finding and selecting a camp site.

Get your pack figured our first, it will cost the most. From there, getting a quality sleeping bag so you are only buying it once and same goes for your mat. Make sure you get an insulated mat and I'd advise in getting an air inflated as it will give you generally around 3" of thickness for about 1lb of weight depending on brand/model etc. Mat insulation is key to making your sleeping bag work to it's best potential.

Once you have this all figured out, you pretty much only need your cook kit and a way to filter water. You could easily do this for $150, even buying new.

[Buzz2401]

Don't be afraid to buy quality products that are used.

[fillthefreezer]

i have to disagree with most, putting pack as a priority. its a huge expense to get something top of the line, and many features are a learned desire. buying something middle of the road is just a waste. get a proven heavy hauler from a backpacking company off ebay, and decide what you do and dont like in a pack, while saving for that holy grail of hunting packs.