Lisbon long term parking - help! :)

Boa tarde! This is my first post, and I'm hoping you knowledgeable Lisboetas may be able to help me with a random question about car parking!

I'm moving from London to Lisboa in October as me and my boyfriend have decided we'd like a change and the opportunity to go freelance in our work. We're very excited, but now trying to sort out all of the smaller details, such as what to do with our car when we get there.. I'm looking for further information or insight into long term parking/parking space rental (and maybe just parking generally - I've tried to do a ton of research, but it's sometimes difficult to find the information simply written!)

We're going to be driving down to Lisbon from London, so we will have our car with us. I know Lisbon isn't an ideal city to own a car in, but then again neither is London and we need it to transport our stuff! Plus we would like to have it during our first couple of months at least so we can go on weekend trips (and probably the odd trip to Ikea to furnish our flat ). Does anyone know of any reasonably priced long term parking places? Our flat is on the Praça das Flores in Principe Real, so ideally not too far away from there, though we're not going to be picky! We'll be working at the Village Underground/LX Factory so nearish to the Alcântara area would be fine too.

The second part of my question is about the feasibility of obtaining a residents parking permit given our GB number plate. I've spent hours trying to research this but haven't been able to find a clear answer on what this entails, other than the sense that this is likely going to be a bureaucratic nightmare. If it's even possible, then I understand we would need a TIF number, however I'm worried that we would then need to start the matriculation process with our car straight away, which I'm not sure we want to do.

Does anyone else have any experience of this, or insight into what the process might be?

Muito obrigada in advance!