What's more important speakers or amplification?

Here is my experience. I started rebuild my system last year. Replaced KEF reference One with B&W 801 new music flow out old CD's. 95' Carver receiver was doing a decent job to drive B&W. Just replaced Carver with an Aragon amp, I do detect some differences but not dramatic changes like replacing speakers. Hope this help.

My opinion would be to work on making the front 2 channels the best possible and keep the Sony receiver on board for amplifying the center and rear speakers and processing duties. Use the pre-out on your receiver to connect the front two channels to another pre and amp or integrated. This could be satisfied by your Jolida if you like that or surf around for someother good integrated amp preferably with a HT passthrough. The Rogue Tempest, Plinius 8150, Manley Stingray, Pathos Classic One, these can all be had for under $1600 used here on Audiogon among others.
Your speakers seem pretty good, although for HT duties I would probably lean towards the Sttaf over the Triangle Titus. But it depends on what you like better. Let me throw out some options depending on what brand you like best. If it is Totem. Sell off all the Traingles and Paradigm's and hopefully this will allow enough fund to invest in a Totem center and surrounds, say the Dreamcatcher series. If you like the Triangle sound better, move the Titus to rear duties (or could sell Titus and keep Pardigms for rears,)sell the Paradigms and the Totems, and with whatever money that leaves you purchase your favorite pair of Triangle speakers within your budget.

Since 80% of home theater sound (dialogue) comes through the center channel, I would focus on the center channel that makes the voices sound the clearest, and most accurate, TO YOU! Once you have found that speaker, it is fairly easy to match the fronts and rears to it as a package.

I have helped several people put together systems after they had spent a lot of money on components and speakers, only to be dissatisfed with the overall effect. In each case I started with the center channel and the end result was a much better, balanced, system. And, much happier people.

I have found that the easiest way to guide someone is to tell them the basics. Some people have stated that without good speakers, no quality sources will sound they way they are supposed too. Or, without good sources no speakeris going to sound the way it is supposed too.

If you have limited resources, ie money, then I would recommend that you start with the speakers. They will last much longer than most electronic components. After getting the best speakers that you can justify, you can then take your time to locate the best match of electronics for that set of speakers.

Ideally, you will be able to locate the speakers and the electronics at the same location and that will give you a chance to decide what you want long term, what the minimum combination you will need to meet your immediate needs, and what your long term goal will be.

For example, I spent more on what I believe to be the best sounding speakers, TO ME, now, and skimped on the AVR. I know that I will upgrade the AVR to a much better system in the future, but I since I auditioned the speakers with the electronics I want for the future, I know that it will sound very good.

I hope that you noticed that I emphasized TO YOU and TO ME. Because, it is what sounds best to you that matters.

It has been my experience that it is much easier to get average speakers to sound good with a great amp than to get great speakers to sound good through a bad amp. I've tried this in home audio, car audio, and pro audio. A key to remember is that your system is only as good as the weakest link, be it your amp or speakers or even cable or interconnects. You'll have to explore your options and decide what will work best for you. As far as brands go that all depends on the type of sound that you like. Go out and audition as many different brands as you can. Stay away from the big chain stores. Small specialized stores are where you usually get the best help.