Hi Zilli how are you?
Looks like you got quite a bombardment from you one query. So glad to hear your bought your first Hi-Fi system. It can be very gratifying listening to your favourite music on a really good system. However getting it home, setting it up and it not sounding anything like you expected it to is not nice.
First off have you made any headway regards the advice people have made? I'd like to think so and that the system is sounding much better. As someone mentioned don't settle for "Getting used to it" if it doesn't impress you to start with something is wrong and of course seeing as it's all new kit it all need to ware it. The Amp, Cables, Speakers and your lovely Deck. even when all is set up correctly you will hear improvments when you replay a record a few months down the line.
If I my add/repeat something, I'm sure to repeat what other people have already said so I apolagise in advance.
Unfortunaly many factors can come in to play regarding your issue. Some basic ones as have already been pointed out are the direction of your speaker cable and do the markings match up. They should be marked with a + or - to help you connect them to the right binding post (not all speaker cable does). As you have bought Bi-Wireable speakers (in my opinion speakers with just 1 positive and 1 negative binding post would have been better as you are not Bi-Amping) you have the question which ones to connect too? As has been pointed out with the bridges in place it shouldn't make a difference which black or which red post you use.
I guess by now you have tried a number of combinations at the speaker end. Looking at the pictures you posted I can see the Bridge (Metal plate) has a circle round the middle post for both red and black posts. I would follow this as you connection points just to be on the safe side.
If it's not been mentioned before the bridge is there to bring the Crossover into play from all 4 binding posts. With out them the speakers wouldn't work correctly with only a twin cable going in. You would either have only the tweeter running (if both connections are Hi +/- or the driver if both connections are Lo +/- Having one in each would result in no sound so the bridge as it suggestes makes this connection and allows the tweeter and driver to work.
In most cases cable has an optimum direction hence the text on the cable and some times arrows depicting the best direction (high end cables). Though it's not a massive differene and some would say no difference, Bi-Wiring the speakers in my opinion will give you more Headroom (openness) and allow you to remove the bridges compleatly. To do this it may be worth getting some Bi-Wire cable or just another pair of what you have. On the second pair you would need spades or open wire to cennect to the amp as you are already using the banana plug socket.
Then making sure the text is going the same way on all stands of the cable (text reading away from the amp towards the speaker) then connecting 2 red marked cables to the same red binding post on the amp and 2 black marked cables to the black binding post on the amp. At the speaker end 1 pair of binding posts as i knid of mentioned is for the drivers in you speaker and the other pair is the tweeters. Bi-Wire cable should be maked telling you the exact posts to bind each strand to.
As mentioned by others a bigger room would be better. Low frequencies have a longer sound wave then the high frequencies and could be masking the high end. If there is any EQ on the Amp may I suggest you don't use it. Set to flat or nutral or bypass it altogether if you can. You would only adding or taking away from the source music. Leave it natural to allow the most detail to come thhrough.
Make sure your Rega deck is on a surface that is 100% flat. That would be a good question to assk you. What do you have your amp and deck mounted on if you haven't already said? Resonece from what they ar standing on can add noise to your music through the speakers so mayby a Quadrespire isolation shelf would be good for your deck to go on.
I hope I have hlped and made sence. For future reference as mentioned by others. Audition what you plan to buy and in my opinion factor the cables you plan to use, Speaker, interconnector and mains cables into your budget. Personally about 1/4-1/3 of your budget should go on cables that will extract the most from your set up and 1/4-1/3 on the furniture you wish to mount it all on. Contact the cable manufacturers, let them know what you have or ar going to purchase kit wise and they should recomend the best cable for your price range. Chord Company are amazing at this and though I'm a CD guy my system has come alive more than I new it could and still I know there is more to come.
Best of luck and sorry for the long post.
The cable Madman.