Dendrite is okay for personal use (a few users), matrix-native, using the better-tested clients. IIRC some bridges work with it, but it doesn't implement the whole appservice API, which blocks you from using some of the better bridges.
I do not recommend synapse if you don't have a lot of memory. I put an extra 8 GB stick in my server for it, bringing it to 14 GB.
It routinely likes to take more than 4GB to itself, though it has become a lot leaner lately.
On the other hand, I was expecting the bridges to me more like Bitlbee which maps personal accounts to IRC rooms. Matrix bridges seem to be more like syncing the content of a room to another.
It sounds like you'd want puppet bridges. Each of your conversations on the remote side has a corresponding room, and what you say in that room is forwarded by the bridge trough your remote account.
You could try out dendrite.matrix.org as a homeserver (btw, dendrite would nicely fit into these 4GB). Most bridges need admin access to the server though, if you want to host them yourself. t2bot.io hosts a few you'd be able to use with your own dendrite, though it hits capacity problems at times.
Finally, you could try to make synapse leaner by not joining big rooms with hundreds of federating servers. There is a max_complexity (something like it) setting for that use case.
I do not recommend synapse if you don't have a lot of memory. I put an extra 8 GB stick in my server for it, bringing it to 14 GB.
It routinely likes to take more than 4GB to itself, though it has become a lot leaner lately.