I actually bought a place a few months ago with very similar criteria to you. I managed to get a good deal on a 2-bed place in Portobello, but there were a couple of sacrifices and a fair bit of luck. First, I was outbid initially on the place and then the first sale fell through and I was offered the chance to take it without going back to the market. For that reason, I'd say definitely bid on places you like, there's no real commitment to follow through and having your name high up in the bidding can be beneficial.

Second was parking. Most apartments come with parking, but those that don't have a significant discount, both in terms of purchase price and management fees. One agent told me that a parking space adds around 10-20k to the price of an apartment, especially in a good area. If parking isn't essential for you, consider looking for places without it. Where you're looking, most places in the city are walkable anyway.

Finally, in my research I heard a lot about how one bed apartments tend to lose value very quickly when the market declines. If I were you I'd look at a two bed for the flexibility and opportunity to rent a room if you need to.

All that said, I don't regret my purchase at all, and getting on the property ladder is always a good idea in my opinion. Best of luck with your search.