No budget? I can definitely work with that...
I can make recommendations on any budget that you have - from cheap to expensive. Most people that I talk to are always on some kind of budget, especially if they have most of the equipment they want to use already. But, since I know you want to do it right, and money is not a problem, lets go through a few ways of doing things, and some products that you may enjoy.
First of all, a 55g standard tank is way too narrow to have a decent aquascape. it would be better to get a larger tank, or a tank that is at minimum 18.5" from front to back. The more I look at tanks, the more I personally enjoy rimless cube acrylic tanks. acrylic is much more clear, and can give you a much better, more natural color instead of looking through glass that has a high iron content. You also spoke of the room being cold. Acrylic is a much better insulator and is able to keep temperature fluctuations down to a minimum, which means more success. Now that we have discussed the tank....
I would go with a sump system and have a space for a mechanical filter, like a filter sock assembly and enough filter socks to change out every two to three days until you can get them washed. The second section should be for a protein skimmer. I prefer Octopus brand protein skimmers on my personal budget, but if you have the money, a bubble king with red dragon pumps would be a good option. In the same chamber of the sump should contain a biopellet reactor - which will process your nitrates and phosphates by providing a carbon source for nitrifying bacteria to grow. It is the most modern way to control it besides water changes. The third chamber would be for the return pump and the auto top off system -- I prefer JBJ brand for $75, but a Tunze Osmolator for $200 will do the same thing.
Talking about heaters, a titanium heater is a must - actually two smaller ones is better then one larger one. I would also get them with controllers so that they won't fail. Heaters always present a challenge as well - since most of them will fail over time and are not fail safe unless you have a backup controller like an Apex to help monitor your temp. Apex units can also control your lights, a calcium reactor, control and monitor your pH - and it has a breakout box that can top off your sump as well. I believe now you can even hook it up to dosing pumps if necessary. Apex controllers allow you also to turn off the pump for feedings - it's only $500 for the unit and another $50 for the pH probe... but it is fun to play with, since you can make changes from your iPhone.
For water flow, you have three options, but I know a Jebao WP is a little on the lower quality side. Tunze makes controllable pumps that start at $225 plus about the same for the controller. However, you could go with a Vortech MP40 and not have wires in the tank - which makes it look pretty sleek. An MP40 is $460 brand new and is money well spent, but I have heard that the customer service isn't as good as Tunze. Flow is very important to get right, and pretty much the more you spend, the better your changes of success with a larger variety of corals, especially more difficult to keep corals.
You should invest in an RO/DI unit for your home as well. you can make pure water from home to top off the tank and to mix your saltwater in... I suggest getting a minimum 5 stage unit from bulk reef and replace two of the stages with refillable catalytic carbon filters and get a refillable DI kit as well - and always keep extra filters on hand. pay attention to your local news to see if they are going to do chlorine burns in the local municipal water supply. That will burn through your catalytic carbon block filters, and the carbon will have to be replaced more rapidly.I would also suggest to get an inline TDS meter with an inlet and outlet monitor... a controller for your unit as well will help you make decisions for when your stuff needs to be replaced. You can put a line into your auto top off reservoir on a float valve as well so that you won't have to worry about having to keep it filled. putting a float valve on a food grade trash can so that it can get filled automatically and you can easily mix saltwater for water changes. putting it on a furniture dolly with wheels would make it easy to get the water over to the tank.
So now you have a few options, and that is a little of what I have learned over the years. Sorry that you felt like I was being rude or condescending. I hope you have a better day, and thank you for reading. See you around the forum.