OK, I wasn't expecting you to go SMD but you seem to have a grip on most of the basics. To cut a long story short I suggest a BC817-40 for the input from the MCU, 100K for the pull up (R1 in my circuit diagram), perhaps 2.2K on the base of the 817, and a DMP3097L-7 for switching the lamp. The latter are £1.85+VAT in a pack of 25 from RS.
Obviously these values don't come from thin air, so to summarise selection:
Start with the load. In round terms we're switching 12V DC @ 2A and we want a P channel MOSFET in SMD packaging. To select a part I put those values in the MOSFET parametric search and order by ascending price before browsing through the list for likely candidates. While I'm browsing the listings I'm bearing few things in mind. Firstly you don't want to buy them buy the reel, you want a small number, if not 1s and 2s you certainly don't want to spend £10+ in total. Secondly the part has to be in stock - this is a key factor at the minute given the disruption in semiconductor supply chains, it's never recovered from COVID. Next the key technical parameter I'm looking at is RDS(ON) since as you identify that's the key for how hot it's going to get in the on condition. To be honest exact values are finger in the ir stuff, I begin with a feeling that a power dissipation of 200mW or so it reasonable for typical SMD transistors so at 2A I want 0.1R or less simply from Ohm's law.
Scanning through the list for likely candidates I arrive at the DMP3097 using the above observations. Open the data sheet and flick through it. Notice it quotes a PD of 1W for a SOT23 package (yes, my preference is deliberately conservative) so our initial assumptions seem fine. No big oddities so that's our one.
Pull up resistor (our R1) is pulled from air with a bit of experience. Input impedance of a MOSFET is going to be very high (10M+) to the extent you can basically call it infinite. That means we can save power with a large value but a bad idea to go really high, if currents get too small leakage and even contamination on the circuit board can start having noticeable effects. 100K chosen as a sensibly high value, may choose to got lower, paossibly down to 47 or even 22K, after all at this level the additional power saving is miniscule.
Low level switching transistor - BC817. That's just my bog standard general purpose SMD NPN. We're not asking it to do anything remotely special here (speed, pwer etc) so I don't even think about it. Go for the -40 variant, it has a higher minimum gain which can save power into the base.
Base resistor. Here I'll consider the properties of what's driving the input but generally figure it's going to be at least TTL compatible in the key metrics - for us that is low voltage is 0.4V or less, high voltage will be 2V or more, don't want to source or sink more than perhaps 1mA. These are generally compatible assumptions for anything from 3.3V CMOS to 5V TTL provided the output isn't driving anything else at the same time. Collector current is insignificant here, but a basic low level switch I tend to plonk in from memory if it's under 100mA or so. The BC817-40 has a gain of at least 250 at that current, so we're looking at 100/250=0.4mA at the base. In the on condition work on the basis the base is at 0.7V and the input is at 2V, that gives 1.3V across the resistor. Again Ohm's law gives 1.3/0.0004 = 3.25K. Call it 2.2K as a standard value that gives us a nice margin even in our worst case conditions.
As for a pull down resistor on the base, generally not with a bipolar transistor and it is the only load on the output. Logic families can allow the "low" voltage to rise up past the switching threshold but at the input, the output is generally far switcher. Since the transistor is either effectively not there when turned off, or pulling it down when turned on, you don't need a pull down to form a potential divider and adjust the switching threshold voltage.
