Larsheen, your broadband options are often dictated by where you live. If you have a Virgin Media cable connection you already have among the highest speed broadband available. You say you have a VM box that is not fit for purpose -- why not, what speed are you getting?
Other options depend on availability and are impossible to predict without an actual test. If you have or can get a phone line, broadband availability will depend on distance to the exchange or fibre-connected kerbside box. Speeds range up to 100 Mbps and down to zero, and costs are in the €40-60 range. You will find lots of different providers but they all have to piggyback on the same copper wire to your house, so you will not find much difference in options between them.
Cellular/mobile data depends on your proximity to a cellular mast and the number of other users in the cell. Performance can vary widely depending on chosen provider, location and time of day. It may go from unusable to several tens of Mbps. You don't want to go for this option unless you know someone nearby with the same provider, or you can get a cancellation/refund on whatever you try. In terms of hardware, you can get a cellular router, a mobile dongle, or you can tether to your phone. You asked about battery impact -- all lithium batteries wear out after a certain number of charge/discharge cycles so yes, heavy usage will affect your battery lifetime. Mobile data is often restricted in terms of monthly usage limits. There are not a lot of options that will let you stream video like you can with a decent cable or landline connection, and where they exist they are in the same price range as those other options.
Fibre-to-the-home (FTTH) is only available in extremely limited areas so let's skip that. There's not really much point talking about satellite either. There may be packet radio providers also, but again completely depends on your location. It's hard to be any more specific without knowing where you live (and I'm not asking) but this is something you can find out yourself by Googling. Also, just because something is available does not mean it will be any good -- it's pathetic but no provider will make any kind of performance guarantee or even that their product is fit for service in your particular location. Hence be very careful about getting locked into contracts unless you understand the local conditions.